"money and capital markets" by miles livingston: a solution and study manual

7/27/2019 "Money and Capital Markets" by Miles Livingston: A Solution and Study Manual

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Money and Capital Markets by Miles

Livingston: A Solution and Study Manual

R.E. Salvino

4329 Thistlewood Terrace

Burtonsville MD 20866

1994-1995, reformatted: 6 Apr 2013

Abstract

This study guide and solution manual is not quite complete and has

not been verified for accuracy, so it is offered in an as is condition. It

was written nearly 20 years ago during a self-study program in finance

in anticipation of a career shift. This career shift never happened and

was the primary reason this study guide and solution manual was not

completed.

Keywords: finance, economics, banking

Table of Contents

Chapter 2: Determinants of Interest Rates ............................. 3

Chapter 3: N eo-Keynesian Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Chapter 4: T he Federal Reserve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1

Chapter 5: I ssuers of Securities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Chapt er 6: Financial Int ermediaries ...................................21

Chapter 7: Bank Regulation and Management . . . . . . . . . . . . . . . . . . . . . . . . 27

Chapter 8: Efficient Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Chapter 9: Spot and Forward Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Chapt er 10: Coupon-Bearing Bonds ...................................44

Chapter 11: Money Market Instruments and Rates . . . . . . . . . . . . . . . . . . . .52Chapter 12: Mortgages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Chapter 13: Bond Investment Risks and Portfolio Strategies . . . . . . . . . . 61

Chapter 14: The Term Structure of Interest Rates . . . . . . . . . . . . . . . . . . . . 65

Current address: 9 Thomson Lane, 15-06 Sky@Eleven, Singapore 297726.

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Chapter 15: International Financial Markets . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Chapter 16: Equities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Chapter 17: Futures Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2

Chapter 18: Financial Futures Contracts ..............................88

Chapter 19: Put and Call Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Chapter 20: Call Features on Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

C h a p t e r 2 1 : D e f a u l t R i s k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 2

Chapter 22: Taxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Chapter 23: Financial Engineering: Specialized Financial Instruments 109

Appendix 1: Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Appendix 2: The Long and Short of It ...............................114

Appendix 3: Notes on Put and Call Options .........................121

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Chapter 2: Determinants of Interest Rates

1. Describe the differences between the classical and loanable funds ap-proaches to the interest rate.

In the classical theory, the money supply does not affect interest rates, theinterest rates are determined solely by business investment and savings byindividuals. The MEI or marginal efficiency of investment (of capital) curveshows the cumulative amount invested as a function of the rate of return(usually stated as showing the rate of return as a function of the cumulativeamount invested); classically, the cost of funds for business is simply theinterest rate, that is, debt is financed with no equity financing. The savings

curve shows the amount of savings by individuals as a function of the rateof return. Classically, the demands for funds comes only from businessinvestment and savings from individuals. Consequently, the interest rateis determined by the intersection of the two curves, in other words by theequation Fmei(i) = Fsave(i) or i = F

1save(Fme(i)).

In the loanable funds approach, the interest rate is determined by the supplyand demand of loanable funds, that is, of the money supply. The consumerand government demands for funds is added to the business demand, andsavings from business and increases in the money supply are added to savingsby individuals. The interest rate is determined by the intersection of thedemand for money as a function of the interest rate D(i) and the supply of

money S(i), that is, by the equation D(i) = S(i) or i = S1(D(i)).

2. What are the major tenets of classical quantity theory and modern quan-tity theory of money? Is velocity a constant in each theory? In practice,what are the determinants of velocity?

In the classical theory, the increase in the money supply for a fixed supply ofgoods results in an increase in the prices of goods. IfM is the money supply,V is the velocity of money (the number of times an average dollar changeshands during a year), P is the price level, and Q is the level of real (physical)output, then MV = PQ (this is basically a definition). The time derivative

of this equation is m+ v = p+ qwhere m = d lnM/dt is the fractional rateof growth in the money supply, v = d lnV/dt is the fractional rate of growthin the velocity, p = d lnP/dt is the fractional rate of growth in the pricelevel, that is, the inflation rate, and q= d lnQ/dt is the fractional rate ofgrowth in real output. These equations are valid in the modern theory also.

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In the classical theory, the velocity V is a constant so that v = 0 and as a

result, m = p + q or p = m q. This means there is inflation whenever themoney supply fractional growth rate is larger than that for real output, thatinflation can be eliminated by adjusting the money supply fractional growthrate to be that for real physical output, and deflation occurs whenever thereal output fractional growth rate is larger than that for the money supply.

In the modern theory, (1) the money supply is the most important determi-nant ofFGNP = PQ and the velocity V is a relatively stable and predictablefunction of economic variables but is not a constant (v = 0); (2) there shouldbe strict rules for government economic policy rather than wide discretion:active tinkering with the money supply is counter-productive since the gov-ernment has a tendency to do the wrong thing; (3) changes in the money

supply have wide ranging impacts upon the economy; (4) fiscal policy (gov-ernment decisions on taxes and spending) has little impact upon the econ-omy, it should focus exclusively on monetary policy (the money supply); (5)an increase in the money supply has 3 impacts which are possibly offsetting:(a) it tends to increase bond prices and lower interest rates, (b) it tends tostimulate output which puts upward pressure on interest rates, (c) it affectsinflationary expectations requiring an inflationary premium to be addedto interest rates for bonds.

3. Assume that the real interest rate r = 3% and that the inflation ratep = 10% with complete certainty and no taxes (t = 0%). Determine the

nominal interest rate.

The nominal rate is given by i = (r +p + rp)/(1 t) = 13.3%.

4. Make the same assumptions as the preceding problem except that thetax rate is t = 28%. Determine the before tax nominal interest rate and thebefore tax real interest rate.

The before tax nominal rate is i = (r + p + rp)/(1 t) = 18.47%, and thebefore tax real rate is r/(1 t) = 4.167%. The remaining term in the beforetax nominal rate is the before tax inflation premium, (p + rp)/(1 t) =14.306%.

5. The nominal rate is i = 15%, the inflation rate is p = 5% and there areno taxes (t = 0%). Assuming complete certainty, the real rate is given byr = (i(1 t)p)/(1 +p) = 9.524%.

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In the following problems, we will assume the risk premium for inflation,

h, is simply given by h = rE(p) where r is the real interest rate and E(p)is the expected rate of inflation. Consequently, the nominal interest rate isgiven by i = (r + E(p) + h)/(1 t) = (r + E(p) + rE(p))/(1 t). For thecase of complete certainty, E(p) = p.

6. Assume no taxes (t = 0%). The market anticipates an inflation rateE(pm) = 8%. The real interest rate, r, is 4%. You anticipate an inflationrate E(p0) = 15%. Explain how you might profit from this information.What is the gain if you are correct?

At time t = 0, borrow $1 at the t = 0 market rate and buy real assets withthe borrowed funds. At t = 1, repay the loan at the locked in t = 0 market

rate (1 + r + E(pm) + rE(pm)) and sell the assets at the t = 1 market rate(1 + r + E(p0) + rE(p0)). The cash flow at t = 0 is 0, and the cash flowat t = 1 is (E(p0) E(pm))(1 + r). If the anticipated inflation rate is thecorrect one, then the gain is 7.28%.

7. Assume no taxes (t = 0%) and complete certainty (E(p) = p). Thenominal interest rate i = 10% and the real rate is r = 5%. What is theinflation rate?

Solving the equation for the nominal interest rate for the inflation rate pgives p = (i(1 t) r)/(1 + r). Substituting the given values yields the

inflation rate p = 4.762%.

8. Assume no taxes (t = 0%). The real interest rate is 5% and the marketanticipates an inflation rate ofE(pm) = 10%. You borrow money and repayit in one period. You used the borrowed funds to buy real assets at timet = 0 and sell the assets at the end of one period, when the loan is repaid.For what actual inflation rate will you make 15.75% ?

The amount borrowed, B, is repaid in one period: R = B(1 + i) where theinterest rate i is i = r+E(pm) +rE(pm). The borrowed funds, B, were usedto get a return A = B(1 + i0) where i0 = r +E(p0) + rE(p0). The total netreturn is AR and, consequently, the net percentage return is (AR)/B =

(E(p0)E(pm))(1+ r). Thus, E(p0) = E(pm) + (AR)/B(1 + r). For thevalues given, (AR)/B = 0.1575, so E(p0) = 25%.

9. Assume no taxes (t = 0%). The nominal interest rate i = 10.25% andthe real interest rate r = 5%. You forecast deflation at a rate E(p0) = 5%

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over the next year. Explain how you could try to profit from your forecast.

What is your profit, if your forecast is correct?

At t = 0, borrow $1 worth of assets, sell them for $1, and lend it out at themarket rate. At time t = 1, you will receive the repayment at the t = 0market rate and you buy back the assets at the t = 1 rate. The cash flowat t = 0 is 0, and the cash flow at t = 1 is (1 + r +E(pm)(1 + r)) (1 + r +E(p0)(1 + r)) = (E(pm)E(p0))(1 + r) which is positive if the forecast fordeflation, E(p0) 0, is correct. First, find E(pm) = (i r)/(1 + r). For thevalues given, E(pm) = 5% and so the profit is 10.5%.

10. Assume complete certainty (E(p) = p) and no taxes (t = 0%). Thenominal interest rate i = 20% and the real interest rate r = 8%. Youforecast that inflation rate is going to be p0 = 18%. You decide to borrow$1 and buy real assets. After one period, you liquidate the real assets andpay off the loan. At what inflation rate would you earn a profit of $0 .12 ?

At t = 0, borrow $1 and buy $1 worth of assets for zero net cash flow att = 0. At t = 1, repay the loan R = 1 + i and receive 1 + r + p0(1 + r)from liquidating the assets. The net return is (1 + r +p0(1 + r)) (1 + i) =(r i) +p0(1 +r) = (p0pm)(1+r) where pm = (ir)/(1 +r) is the marketinflation rate at t = 0. Since pm = 11.11111%, to get a net return of $0.12on a dollar or 12%, the inflation rate must be p0 = 22.22222% = 2pm.

11. Assume no taxes. The market forecasts an inflation rate E(pm) = 5%.You forecast an inflation rate ofE(p0) = 15%. You decide to borrow $1 andinvest in real assets for one period. Your forecast equals the actual inflationrate. When you sell the assets and repay the loan, you earn a profit of $0.11.What is the real interest rate?

The cash flow at time t = 0 is zero; the cash flow at time t = 1 consists ofthe return on the dollar investment (1 + r + E(p0)(1 + r)) less the amountneeded to repay the loan (1 + r + E(pm)(1 + r)) for a net cash flow of(E(p0) E(pm))(1 + r). Since this net cash flow is the net profit for thetransaction, this is equal to 11%, so the the real interest rate r is given byr =(net profit)/(E(p0) E(pm)) 1 = 10%.

12. Assume no taxes. The nominal interest rate is observed to be 20%.What is the lowest possible value for the sum of the real interest rate r andthe inflation rate p?

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Since i = (r +p) + rp, then (i (r +p))2 = (rp)2 0, so that the minimum

value occurs for (i (r + p)min)2

= 0, or (r + p)min = i. In this case, theminimum numerical value is 20%.

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Chapter 3: Neo-Keynesian Model

1. Explain relationship between marginal propensity to consume (fmpc) andthe multiplier.

The multiplier has a simple inverse relationship to the marginal propensityto save fmps, multiplier = 1/fmps. The marginal propensity to save has asimple linear relationship to the marginal propensity to consume, fmps =1 fmpc. Consequently, the multiplier has an inverse linear relationshipto fmpc, multiplier = 1/(1 fmpc). As fmpc approaches 1 from below, themultiplier becomes arbitrarily large and positive; as fmpc approaches 0 fromabove, the multiplier approaches 1.

2. In the neo-Keynesian model, what determines the total demand formoney?

The total demand for money is the sum of transactions demand (the exactmatching of cash inflows and cash outflows by business is usually not pos-sible, resulting in transaction balances), speculative demand (cash balancesheld to buy securities in the future at lower, more attractive prices), andprecautionary balances (cash balances kept as precautions against transac-tion balances running short, emergency funds). Usually, precautionarybalances are neglected in neo-Keynesian analyses.

3. If government spending increases in the neo-Keynesian approach, whatis the impact upon interest rates?

The IS curve generates the GNP as a function of interest rates from theincome point of view, YIS(i). The LM curve generates the GNP as a functionof interest rates from the demand for money point of view, YLM(i). Theequilibrium interest rate is determined by the equation YIS(i) = YLM(i).An increase in government spending shifts the YIS(i) curve to the right,that is, for a given interest rate i, YIS(i) increases but leaves the LM curveunchanged. The intersection with the YLM(i) curve will change, dependingon the shape of the LM curve.

If the LM curve has a positive slope in the region of intersection with the IScurve, dYLM(i)/di > 0, then an increase of government spending increasesinterest rates (the intersection of the IS and LM curve occurs at a larger valueof i) and some business investment is crowded out of the market. If the LM

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curve is flat in the region of intersection with the IS curve, dYLM(i)/di = 0,

then an increase of government spending has no affect on interest rates (theintersection of the IS and LM curves occurs at the same value of interestrate i) and no private business is crowded out of the market. Finally, if theLM curve has a vertical slope in the region of intersection with the IS curve,dYLM(i)/di , then an increase in government spending increases theinterest rate (the intersection of the IS and LM curves occurs at a largervalue of interest rate i) and crowds out enough business investment to offsetthe change in government spending.

4. If the money supply is increased in the neo-Keynesian model, explain theimpact upon interest rates.

An increase in the money supply shifts the LM curve to the right, that is,for a given interest rate i, YLM(i) increases in regions where the LM curveis not flat. The IS curve is unchanged and the intersection of the LM curvewith the IS curve which determines the equilibrium interest rate changesdepending on the shapes of the IS and LM curves.

Since dYIS(i)/di 0, if dYLM(i)/di > 0 in the region of intersection withthe IS curve, an increase in the money supply will lower the interest rate(the intersection of curves occurs at a lower interest rate) as long as the IScurve is not flat; if the IS curve is flat, then there is no change on the interestrate (intersection of curves occurs at same interest rate); if the IS curve isvertical in the region of intersection with the LM curve, dYIS(i)/di ,then there is a decrease in the interest rates (the curves intersect at a lowervalue of interest rate i). IfdYLM(i)/di = 0 in the region of intersection withthe IS curve, there is no effect on the interest rate (the intersection of curvesoccurs at the same interest rate): this is known as the liquidity trap, andhas not yet been observed to occur in the U.S.

5. According to the Modern Monetarist approach, an increase in the moneysupply increases inflationary expectations. Show how an increase in infla-tionary expectations may be incorporated into the neo-Keynesian model.

Probably the simplest way to do this is to assume the standard neo-Keynesian

approach determines the real interest rate r, rather than the nominal inter-est rate i. We then determine the expected rate of inflation, E(p), by themoney supply and construct the nominal rate from i = r + E(p)(1 + r).

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Appendix: IS and LM Curves

The IS curve, YIS(i) or iIS(Y), is generated geometrically from a sequenceof four graphs. First, one uses the FMEI(i) + G(i) curve to obtain a valueof J = I + G (investment plus government spending) that corresponds toa specified value of interest rate. Second, that value of J = I + G is usedto obtain a corresponding value of R = S + T (savings plus taxes): inthe simplest case, J = R because aggregate expenditures E = C + I + Gand aggregate income Y = C+ S+ T, where C is consumer expenditures.The condition for equilibrium is aggregate expenditures equals aggregateincome, E = Y, which simplifies to J = R in this case. Third, that valueof R = S+ T is added to C to obtain Y which corresponds to the value of

interest rate i, giving the fourth graph YIS(i) or iIS(Y).

The LM curve, YLM(i) or iLM(Y), is generated geometrically from a se-quence of four different graphs. First, one uses the speculative demand formoney curve, MS(i) or i(MS), to obtain a value for MS that corresponds toa specified value of interest rate. Second, that value of MS is then used toobtain a corresponding value for transaction balances since MT = M MSwhere M is the total money supply. Third, that transaction balance is usedto obtain a corresponding FGNP = Y by means of the modified equation ofexchange MTV = Y since Y = P Q = FGNP. This value ofY correspondsto the value of interest rate i, giving the fourth graph YLM(i) or iLM(Y).

It is the intersection of these curves which determines the equilibrium inter-est rate, YIS(i) = YLM(i) or the equilibrium GNP, iIS(Y) = iLM(Y). Thesemay be stated as i = Y1

1(Y2(i)) and Y = i

1

1(i2(Y)) where the subscripts

1 and 2 could be either IS or LM.

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Chapter 4: Federal Reserve

1. Describe the composition and role of the Federal Open Market Committee(FOMC).

The FOMC is composed of the 7 governors of the Board of Governors of theFederal Reserve, the president of the federal reserve district bank of NY,and four presidents of from the remaining 11 federal reserve district banks(who serve on a rotating basis).

The primary task of the FOMC is to draft a monetary policy directive whichsets guidelines for the growth rate of the money supply and the level of

interest rates. This is kept secret for 6 weeks after a meeting of the FOMC.

2. Why are there several measures of the money supply? What are themajor differences between M1, M2, and M3?

What constitutes money is not completely clear, although money shouldhave 3 main characteristics: (1) it should be a medium of exchange, (2) itshould be a unit of account, and (3) it should have a store of value. But sincethere is no easy answer to the question of what is money, several measureshave been adopted: M1, M2, and M3.

M1 includes coins and currency in circulation, travelers checks, plus privatebank deposits upon which checks can be written. M2 includes M1 and addsmost types of personal savings accounts (including money market fundsand money market deposit accounts at banks), CDs of less than $100, 000,overnight repurchase agreements, overnight Eurodollars, and money marketmutual funds held by individuals. M3 includes M2 and adds CDs of morethan $100, 000, repurchase agreements for longer than overnight, Eurodollarsfor longer than overnight, and institutional money market mutual funds.

3. Explain the impact of reduction in required reserves on the money supply.

The reduction of required reserves in effect produces excess reserves, freeingup the excess by making them available to the individual banks and thus

increasing the money supply. This tends to decrease interest rates sincethere is more money available and stimulates economic activity.

On the other hand, an increase in required reserves freezes the excessreserves and makes less money available to banks for lending, thus decreasing

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the money supply. This tends to increase interest rates and depress or slow

down economic activity.

4. What are the functions of the federal discount window?

It allows the Federal Reserve to be a lender of last resort to banks inneed. In the commercial loan theory, the central federal district bank con-trols the economy by making loans to commercial banks backed by loansto businesses. This is an incorrect view since short-term business loans arenot self-liquidating when economy-wide recessions or depressions occur andmany firms are unable to sell their inventory and repay their short-termloans in full.

It is still a tool, however, of a lender of last resort, providing funds toindividual banks or to the banking system as a whole at times when fundsare short. It acts as an injector of funds, controlling the money supply bycontrolling the discount window interest rate.

Changes in the discount rate follows the trend, it doesnt set the trend: whenthe Fed eases monetary conditions by buying T-bills (increasing the moneysupply), short-term interest rates (including federal funds rate) decline, andthen somewhat later the discount rate is lowered. When the Fed hardens themonetary conditions by selling or not buying T-bills (decreasing the moneysupply), short-term interest rates (including federal funds rate) increase, andsomewhat later the discount rate is increased.

5. Describe the relationship between the discount rate and other moneymarket rates.

As stated in the answer to question 4, changes in the discount rate tend tolag behind other interest rates (such as federal funds rate, the rate at whichbanks lend to other banks) rather than to set the trend. However, there aretimes when discount rate changes are surprises and reveal new informationabout Federal Reserve policy decisions.

As short-term interest rates decrease (due to an increase in the money sup-ply), the discount rate decreases since fewer funds will need to be borrowed.As short-term interest rates increase (due to a decrease in the money sup-

ply) the discount rate increases since more funds will need to be borrowed.The increase is meant to discourage borrowing and thus to slow down thelevel of economic activity.

6. Why are open market operations the primary tool of monetary policy?

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Open market operations involve the purchase and sale of US Treasury secu-

rities in the open market by the Federal Reserve. If the Fed buys securitiesfrom individuals, the money supply is increased (tending to decrease in-terest rates); if the Fed sells securities to individuals, the money supply isdecreased (tending to increase interest rates); if the Fed buys securities fromcommercial banks, it creates excess reserves for the banks that can be with-drawn and thus increasing the money supply; if the Fed sells securities tocommercial banks, it creates negative reserves for the banks that must befilled and thus decreases the money supply.

In practice, the Fed has unlimited buying power since it can create money.It tends to maintain a large portfolio of US Treasury securities which earnsinterest: part of this interest is used to pay for operating expenses of the

Fed, the remainder is put back into the US Treasury.

7. Explain the procedure for collecting a check drawn on a bank in onFederal Reserve district and deposited in another Federal Reserve district.

The local bank in district A (where the check is deposited) accepts the checkand sends the check to the Federal Reserve Bank for district A. The FederalReserve Bank for district A transmits the check to the Federal Reserve Bankfor district B, which sends the check to the local bank in district B (wherethe check was drawn) for payment. The Federal Reserve then transmitspayment to the local bank in district A. The process typically takes severaldays.

8. What is the advantage of a local clearinghouse for check collection?

The clearinghouse can settle all checks drawn on participating banks, can-celling out some of the interbank transfers of funds. This allows the netshifts of funds between participating banks to be made efficiently.

9. One of the functions of the Federal Reserve is to regulate security credit.What is the motivation behind this regulation?

There is a concern that excessive use of security credit (buying on margin)

might contribute to boom and bust cycles in security prices and in the overalleconomy. A buyer of common stock is required to put down a minimum ofX% of the original purchase price in a margin account. The value of Xdepends on the type of security being purchased on margin.

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The use of borrowed funds to buy securities is a form of financial lever-

age: fractional changes in a levered or margined position are greater thanfractional changes in the underlying security. The fractional change in theleveraged position is equal to the fractional change in the underlying secu-rity divided by the fraction of the underlying security price put down ( f),

PlevPlev

=PsecPsecf

(0.1)

10. Reserve requirements on bank deposits are 5% and there are no leakagessuch as cash withdrawals. Banks receive an injection of $1, 000 in excess

reserves. Determine the increase in the money supply if all excess reservescan be lent out.

Define the following quantities for the nth deposit: excess reserves Rex(n),additional loans Ladd(n), additional required reserves Radd(n), and totaldeposits Dtot(n). Since all excess reserves are lent out, Ladd(n) = Rex(n). Ifx is the fractional reserve requirement on bank deposits, then the followingequations hold:

Rex(n + 1) = Rex(n) Radd(n)

Radd(n) = xRex(n)

Rex(n + 1) = (1 x)Rex(n) = (1 x)nRex(0)

Dtot(n) =n

j=1

Rex(j) = Rex(0)n

j=1

(1 x)j1

Dtot(n) is the increase in the money supply. The sum can be evaluated:since (1 x) < 1 for 0 x < 1, this is a simple geometric series and yields

Dtot(n) =Rex(0)

x (1 (1 x)n)

In the limit n , the increase in the money supply becomes Dtot() =Rex(0)/x. In the particular case of x = 0.05 and Rex(0) = $1, 000, theincrease in the money supply is $20, 000.

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11. Assume single bank economy with very strong loan demand and all

money held as checking deposits. The money supply, Mi, is initially $200, 000.The Fed buys $10, 000 worth of bonds from the bank. The money supplyincreases to Mf = $300, 000. What is the reserve requirement, x ?

The increase in the money supply is Dtot() = Mf Mi = $100, 000. Theinjection into the supply is Rex(0) = $10, 000. Consequently, the reserverequirement is x = Rex(0)/Dtot() = 0.10 = 10%.

12. Make the same assumptions as in problem 11. The initial money supplyis Mi = $100, 000. The Fed increases the reserve requirement by 2% andthe money supply drops to Mf = $50, 000. What percent is the new reserverequirement?

The change in the money supply is Dtot() = Mf Mi = $50, 000. Theinjection is Rex(0) = 0.02 $100, 000 = $2, 000. The new reserverequirement x is given by Rex(0)/Dtot() = 0.04. So, the new require-ment is 4%, and since the requirement increase was 2%, the initial reserverequirement was 2%.

13. You purchase $5, 000 worth of securities by putting down a margin of25%. Compute the fractional gains and losses of the margined position if theunderlying security (a) increases by 10% and (b) decreases by 20%. Assumethe broker has a rule to give a margin call when the equity of the leveraged

position is worth 10% of the underlying security. At what point would themargin call occur?

In all cases, f = 0.25. In case (a), Psec/Psec = 0.10 and in case (b)Psec/Psec = 0.20. Since Plev/Plev is given by the fractional changein the underlying security divided by f, Psec/(Psecf), so for case (a)Plev/Plev = 0.40 = 40% and for case (b) Plev/Plev = 0.8 = 80%.

If the margin call occurs when the leveraged position has only 10% equityremaining in the underlying security, then the change in the leveraged po-sition is 90%. So the margin call will come when the underlying securityhas changed by 0.9f = 0.225 = 22.5%.

14. Assume a margin requirement of 40% of the purchase price of a security.Neglecting any current interest or dividends, determine the fractional changein the underlying security if your equity changes by 25%.

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Solving for the fractional change in the underlying security, we find that

Psec/Psec = f Plev/Plev. Substituting the numerical values, the frac-tional change in the underlying security is 0.10 or 10%.

15. The Fed regulates margin requirements for security purchases. Assumethat the margin requirement (percent put down) is X% (or a fraction off = X/100). A speculator buys a security for $300 and the security doublesin price. What is the rate of increase in the speculators equity?

The fractional change in the underlying security is 1 (($600 $300) dividedby $300). The change in the leveraged or margined position is 1/f = 100/Xwhere X is expressed as a percent.

16. Three banks in a city - Barnett Bank, Sun Bank, and First Union Bank- establish a clearinghouse to handle all interbank checks. Compute the netinterbank transfers required to net out all these checks.

Written on Barnett Sun First Union Total Written

Barnett 0 300 500 800Sun 100 0 400 500First Union 500 400 0 900

Total Deposits 600 700 900 2200Total Written 800 500 900 2200

Net Deposits 200 200 0 0

17. Three banks in Chicago established a clearinghouse for their checkswritten against each other. Determine the net transfers of funds to settleall these checks?

Written on First Second Third Total Written

First 0 100 800 900Second 200 0 600 800Third 300 700 0 1000

Total Deposits 500 800 1400 2700Total Written 900 800 1000 2700

Net Deposits 400 0 400 0

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Chapter 5: Issuers of Securities

1. Since 1980, the market for Treasury debt has become increasingly impor-tant. Why?

Since 1980, annual deficits of over $100 billion have become the norm. Thetotal marketable debt (financeable by debt securities) has ballooned to about$3 trillion, while non-marketable debt adds about another $1 trillion. Theenormous growth of federal debt increases the importance of Treasury debtsecurities in the debt market.

2. What types of entities are major holders of Treasury securities and why?

There are 5 major classes of Treasury security holders:

(1) the Federal Reserve, in order to control monetary conditions, musthave sizable holdings of US Treasury securities,

(2) commercial banks have holdings as secondary reserves, assets that canbe readily turned into cash as the need arises,

(3) individual investors (private, domestic, nonfinancial) have Treasuriessince they are default-free, free of state and local income taxes, andhighly marketable,

(4) foreigners have Treasuries since they are default-free, are denominatedin US dollars which is a relatively safe currency, and

(5) nonbank financial institutions (private, nonbank, financial)

They all hold Treasuries for the same reasons as commercial banks andindividual investors.

3. Explain the procedure by which the Treasury auctions securities. Whatare the pros and cons for using this type of auction?

Treasury securities are sold in weekly auctions. These auctions require sealedbids by a specified time, and are either of a competitive or noncompetitivenature.

A noncompetitive bid does not specify a price, it merely specifies the parvalue (face value) of the securities desired and implicitly agrees to accept the

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weighted average price of all accepted competitive bids: all noncompetitive

bids are accepted by the Treasury.The Treasury accepts competitive bids with the highest prices and lowestinterest rates. Since the bidding is sealed and not open, different prices willbe paid by different purchasers for equivalent securities.

The main advantage of this type of auction for the Treasury is that it willreceive higher total proceeds than for an open auction. The main disad-vantage is for the investors: it is actually an unfair process since differentbuyers of the same security will pay different prices. In practice, the differ-ence between the highest and lowest accepted bids tends to be small, thatis, the demand curve tends to be flat since new issues must be competitivelypriced relative to traded old issues.

4. Treasury announces an auction of $10 billion par value of 52 week T-bills.$2 billion of noncompetitive bids are received. The competitive bids are asfollows:

Price/$ of Par Par Value Fraction

0.9200 $3 billion 0.16670.9194 $3 billion 0.16670.9188 $4 billion 0.22220.9180 $2 billion 0.11110.9178 $6 billion 0.3333

$18 billion 1.00

Compute the price per dollar of par paid by noncompetitive bidders.

The third column above, Fraction, is the par value divided by the total parvalue of the auction. The price paid by the noncompetitive bidders is theweighted price of the accepted bids, that is,

Pnon =

i

FiPi

where Fi is the fraction listed in the third column above, and Pi is theprice per dollar of par of the accepted bids given in the first column above.Consequently, the price paid per dollar of par by the noncompetitive bidders

is Pnon = 0.9187.

5. Treasury announces an auction of $12 billion par value of 52 week T-bills.$3 billion of noncompetitive bids are received. The competitive bids are asfollows:

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Amount of Bid ($ M) Price/$ of Par Bid Fraction

5.0 0.9200 0.357144.0 0.9180 0.285713.0 0.9170 0.214282.0 0.9160 0.14286

14.0 1.00

What is the price paid per $1 of par (to 4 decimal places) by noncompetitivebidders?

Par Value ($ M) Par Value Fraction

5.43478 0.356454.35730 0.285783.27154 0.21457

2.18341 0.1432015.24703 1.00

The weighted average using the bid fraction as the weights for the price perdollar of par gives Pnon = 0.9182 per dollar of par; the weighted averageusing the par value fraction as the weights for the price per dollar of pargives Pnon = 0.9182 per dollar of par. Thus, to 4 decimal places, it does notmatter which weights are used in calculating the weighted average price perdollar of par.

6. What are the advantages and disadvantages for a corporation to issuebonds as opposed to selling equity or retained earnings?

If a corporation does extremely well, all incremental returns above paymentsto bondholders go to stockholders who earn high returns; if the corporationdoes poorly, ther may be little or nothing left for stockholders after payingfixed obligations to bondholders. Returns to stockholders contain a magnifi-cation effect: if firm does well, stockholders do very well; if firm does poorly,stockholders do very poorly. In other words, equity is more volatile thandebt obligations (bonds) and bonds may have a larger market if there aremore risk-averse investors willing to forgo large gains if the firm does verywell; equity will be more attractive to risk-seeking investors. In addition,there may be tax advantages for debt obligations which are absent for equity

considerations.If managers of a firm have better information about the firms prospectsthan the markets do (asymmetric information), the stock price of the firmmay not reflect profits from new opportunities and may be relatively low

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compared to what it should be - sale of stock at such a low price would be

a mistake, and issuing debt obligations (bonds) would be a better idea.Mention should be made of the agency problem: stockholders typically hiremanagers to act as agents on their behalf, but the gain to the agent fromcorporate strategy may be different from the gain to the stockholders. Ra-tional agents may be expected to act in their own personal interest eventhough their professional obligations require them to act for the interest ofthe stockholders.

7. What does the term securitization mean?

Securitization is the process of selling financial quantities (e.g., mortgages)

which effectively changes the financial quantity into a security that can bebought and sold in the resale market.

Originators of the financial quantity no longer bear the risk of default onrepayment or risk that interest rates might change adversely in the future- risks are borne by the purchaser of the financial quantity. This opensup the market for a financial quantity to more originators, increasing theavailability of funds to the market for the particular financial quantity andreducing interest costs to borrowers.

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Chapter 6: Financial Intermediaries

1. Describe the reasons why financial intermediaries exist.

The basic reasons for the existence of financial intermediaries are:

(1) they expedite the flow of funds from sectors with surpluses to sectorswith deficits

(2) they expedite the flow of savings from savers to investors in capitalequipment

(3) they expedite the flow in cases where direct investment is inefficient,undesirable, or impossible

(4) they make efficient use of transaction balances (the funds held becauseof difficulties for firms and individuals to exactly match inflows andoutflows of funds) held as demand deposits in banks, pooled together

(5) they make the process of issuing securities easier so that more issuersare able to raise funds (investment bankers)

(6) they aid in making the resale or secondary market for securities moreefficient (brokers and dealers)

(7) they distribute risk among a large population of insured individuals orfirms (insurance companies)

(8) they can pool small savings

(9) they can diversify risk

(10) they have economies of scale in monitoring information and evaluatinginvestment risk

(11) they can lower transaction costs

2. Explain the meaning of the term diversification. Under what circum-stances is there a benefit in diversifying?

Diversification is a process by which risks are spread out among many dif-ferent investments. For instance, a large investor can spread the risk of

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default over many loans, so even if some loans are not repaid, the entire

portfolio of investments still makes a profit; a small investor can not spreadrisk as much and is at greater risk of suffering devastating losses in case ofdefault. The only case where diversifying is not beneficial is in the case ofabsolute certainty with regard to the desired behavior of the investment, amost unlikely case.

3. What role do investment bankers play in the financial system? What arethe economic benefits of investment bankers?

(1) Investment banking firms are engaged in the marketing of securitieswhen they are originally sold (competitive bidding at auctions or ne-gotiated offerings)

(2) they expedite the sale for original sale of securities in the primary ornew issue market (the resale market is frequently called the secondarymarket

(3) underwriting: the outright purchase of an entire security issue by theinvestment banker (or syndicate) which takes the risk of reselling theissue to the public, earning the difference in prices as an underwritingfee or spread (part of the underwriting fee is compensation for the riskof having to sell below the purchase price)

(4) shelf registration: securities are effectively preregistered with the SEC

and once approved the issue can be brought to market on very shortnotice, permitting the issuer to time the issue as market conditionschange (without preregistration, public registration may take severalweeks)

(5) underwriter prefers low bid on first issue (below fair market value) soit can rapidly sell the issue in the open market (the incentives of theunderwriter conflict with the incentives of the issuing firm)

(6) best efforts selling: try to sell as much as possible of an issue, withany unsold amount reverting back to issuing firm; this procedure isconcentrated in the low and high risk offerings - low risk issues do not

needan underwriter to absorb a risk, and the underwriter is unwillingto assume the risk for high risk securities (best selling is a low riskprocess for an investment banking firm)

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(7) private offering: the direct selling of securities by corporations to buy-

ers (e.g., corporate bond issue to an insurance company) - (a) no reg-istration cost for public offering, (b) can be tailor made to fit needs ofissuer and buyer, (c) can not be widely traded, the resale market forprivate offerings is limited (illiquid), and (d) the interest rate for pri-vate offerings is higher than an identical public offering (disadvantageto issuer, advantage to buyer)

4. Why has investment banking been separated from banking? Are thereany disadvantages of separating the two?

Investment bankers are marketers of securities and are not banks: the Glass-

Steagall Act of 1933 prohibited banks from investment banking.

(1) banks might be able to use bank funds to manipulate security prices

(2) it is possible that the ups and downs of the stock market prices mightadversely affect the stability of the banking system

(3) banks are regulated and so might have an unfair advantage over non-regulated, nonprotected investment bankers, brokers, and dealers (couldseparate regulated from nonregulated parts of the bank, but wouldprobably be unlikely in practice)

There has been a trend to whittle away at the Glass-Steagall prohibition.

(1) nonbanks have increasingly been allowed to engage in banking activ-ities without the burden of regulation imposed on banks - why notpermit banks some investment banking activities?

(2) other industrialized nations have less separation of banking from otherfinancial intermediaries

5. Describe various types of orders for securities, including market order,limit order, stop order, and a shortsale.

The resale or secondary market is run by brokers and dealers. It is usuallydouble auction where buyers and sellers submit bids simultaneously and allparticipants are aware of everyone elses bids, submitted continuously.For an English auction, the price is raised in an open and oral auction until

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only a single bidder remains. Trading takes place on organized exchanges

(NYSE, AMEX: the first and second largest by volume of trading), membersof exchanges are said to have a seat on the exchange. Exchange seatsthemselves are traded and their market value fluctuates as market conditionschange. The types of exchange members are: (a) commission brokers, thelargest group, (b) odd-lot brokers for transactions involving an amount ofless than 100 shares, (c) a registered trader who trades for his/her ownaccount, and (d) specialist firms, market makers for individual securitieslisted on the exchange.

There are listing requirements a firm must meet in order for its stock to betraded on an exchange: a minimum size, a minimum number of shareholders,and a minimum period of existence. The Third Market is the Over The

Counter (OTC) market, a network of dealers who make markets in individualsecurities. A sizable volume of stock trading occurs in the OTC market, aswell as virtually all bond volume. Dealers are highly levered, their equity isa small percentage of the market value of their inventory of securities (theyhave some debt financing in the form of bank loans, most is in the form ofrepos).

A repurchase agreement (repo) is the sale of a US Treasury security withan agreement to repurchase the same security the next day at the sale priceplus overnight interest. If the agreement is for longer than overnight, it iscalled a term repo. Positioning refers to gambling on the direction ofprice movements: for example, a bond dealer buys bonds in expectation of

lower interest rates and consequent higher prices for the purchase bonds (ifwrong, the dealer closes the position at unfavorable prices and takes a loss).Options and futures are traded on organized exchanges, but a clearinghouseis required to guarantee performance since participants may have financialliabilities exceeding their original cash committments.

market order - commission broker executes order at most favorableprice at time order hits the exchange floor (the order will definitely becarried out, but price may change adversely by time order is carriedout)

limit order - an order with constraints, the order will be executedonly if constraints are met (it can be left outstanding indefinitely untilconstraints are met or it can be canceled if not executed immediatelyas a fill or kill order)

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stop order - an order to close out an existing position if certain condi-

tions are met (e.g., buy at $40 but sell at $37)

shortsale - a security is borrowed and sold with the expectation ofbuying back the security at a later time for a lower price to return tothe lender (borrowing to sell high and buy low); the proceeds from ashortsale must be left on deposit with the broker, and the shortsellermust pay any cash dividends from the security to the lender of thesecurity

6. What are the pros and cons of having a specialist system of marketmaking?

pro: the purpose is to reduce the variability of security prices: whentoo many sellers exist, the specialist buys to keep prices from fallingtoo low; when too many buyers exist, the specialist sells to preventprices from rising too high (the price protection is meant over theshort term)

pro: it is a monopoly position, since every listed security has oneand only one specialist for that security, which is supposedly the mostefficient method of stabilizing prices over the short term

con: SEC evidence indicates very high profits for specialist firms

con: specialists have the right to request suspension of trading whenbuy and sell orders are allegedly imbalanced: but profit incentives ofspecialist firms conflict with its role as stabilizer of prices (why buyat dropping prices, postpone until prices have completed their drop);comparison with OTC shows that trades continued on securities thatwere stopped by specialists on NYSE

7. Explain economic reasons for the existence of bid-asked spreads.

The bid-price is the price at which dealers are willing to buy; the asked-price

is the price at which dealers are willing to sell. The bid-asked spread is thedifference between bid and asked prices and represents the price of dealerservices and are related to risks borne by dealers.

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(1) they are inversely related to the volume of trading (a large spread for a

thin market or low volume market), an inactive resale market implieslonger holding periods for the dealer and a consequent greater chanceof a price change (the likelihood of an unfavorable event increases withincreasing holding periods).

(2) they are positively related to the inherent price risk of individual se-curities: the bid-asked spread is smaller on less risky investments thanon higher risk investments

(3) the spread should be a function of dealer financing costs: high spreadsfor high interest rates, low spreads for low rates, reflecting the cost offinancing the inventory of securities

(4) the spread may depend on the possibility that the dealer is tradingagainst an informed investor who knows more than the dealer, whichis an incentive to widen the spread

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Chapter 7: Bank Regulation and Management

1. What is the difference between a commercial bank and a savings andloan?

A commercial bank in an institution which offers checking deposits andmakes commercial loans; a savings and loan, or thrift, have no checkingaccounts and are primarily restricted to real estate loans. Thrifts haverecently been permitted to off checking accounts and to make more non-realestate loans, blurring the distinction between commercial banks and savingsand loans.

2. What are the motivations for regulating banks? There has been a trendtoward deregulation in recent years. Why?

The three main motivations behind bank regulation are:

(1) bank safety is considered essential, that bank depositors should notbe regarded as creditors who bear the risk of default: insured depositsrequires bank regulation

(2) the fear that bank failures will seriously damage local economies andeven the overall economy

(3) it is essential to maintaining competition, reflecting a concern aboutthe extremes of too few or too many banks: a monopoly or oligopolywhich controls the market in the first case, cut-throat competitionresulting in many failures in the second case.

The recent trend toward deregulation: . . . For the most part, it seems thatderegulation is just a form of disguised regulation. Its not a conflict ofregulation versus deregulation but my regulations versus your regula-tions. This, of course, is not the standard view of deregulation.

3. What are the practical differences if a bank has a national charter asopposed to a state charter?

A national charter is granted by the Comptroller of Currency; a state charteris granted by the state regulatory authorities. The difference has blurredin recent years as restrictions have been eased: interstate banking has beenpermitted for states agreeing to interstate reciprocal branching.

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4. Explain intrastate and interstate bank branching restrictions.

Intrastate bank branching limits the banks ability to create branches withina state: (1) unit banking allows only one bank office, (2) limited branchingallows branches in areas approved by the state banking authorities, and (3)unrestricted branching permits offices anywhere in the state.

Interstate bank branching enables banks to have offices in more thanone state. This is permitted by a national charter or, in a more restrictedsense, by state chartered banks with reciprocal agreements allowing branch-ing across specified state lines.

5. FDIC insurance fees are a fixed percentage. How might this affect risktaking attitudes of bank management?

A poorly managed, high-risk bank with low quality loans pays the sameinsurance rate as a well managed low-risk bank with high quality loans. Thisflat rate insurance fee gives incentives to take on high risk loans which carryhigh interest rates since the rewards for success are high and the penalty forfailure is small.

6. What is the purpose of bank examinations? If a problem bank does notimprove its performance, what courses of action are available to regulators?

The purpose of bank examinations is to maintain good loan quality and

to prevent fraud and embezzlement. Banks with problems are put on aproblem list and monitored more closely. If performance does not improve,regulators have 6 courses of action they can take: (1) issue cease and desistorders prohibiting the bank from a specific activity, (2) levy fines of up to$10, 000 per day, (3) remove the managers of the bank, (4) revoke the bankscharter, forcing the bank to cease operations, (5) stop insurance coverageby FDIC, and (6) deny access to the Feds discount window, wire transfersystem, and check collection facilities.

7. If a bank fails, how can FDIC handle the situation?

FDIC can handle the situation in one of three basic ways: (1) try to arrange a

merger with a more sound financial institution, compensating the acquiringbank to make the merger feasible, (2) pay off insured depositors and liquidateassets, using the residual proceeds to pay off uninsured depositors, and (3)take over the failed institution and operate it.

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8. Why do banks hold cash and marketable securities?

Banks must hold cash to meet the needs of its customers, to expedite anumber of transactions such as check clearing, and to meet reserve require-ments set by the Fed. Banks hold marketable securities, such as short termfixed income securities (large US Treasury securities), as secondary reserves:highly liquid assets available to sell rapidly if the need for cash arises. Thebank may also hold municipal bonds of municipalities served by the bank,typically a customer of the bank, partly because such bonds are exemptfrom income taxes.

9. Explain why default risk raises the interest rate on a loan.

Loans are major earning assets of banks, a major share of bank revenuescome from interest on loans. A premium to compensate the bank for defaultrisk is a higher interest rate, set high enough to allow for expected lossesfrom default on some loans. If the bank portfolio of loans reflects the defaultrisks of its customers, on average, it should make a profit on its loans.

10. Why is diversification of a loan portfolio important to a bank?

If a bank makes loans to a single sector or industry and that sector orindustry does poorly as a whole, many bank loans may default resulting inexcessive losses to the bank. Diversification lessens the impact of widespreaddefault in a given sector or industry.

11. What risk reduction alternatives are available to a bank faced withvariable interest rates on its sources of funds?

The five main risk reduction alternatives are:

(1) make relatively short term business and nonmortgage consumer loans

(2) match maturities of loans (bank assets) and financing (bank liabilities):e.g., a 6 month loan to a construction company at 12% financed with6 month certificates of deposit at 9%, locking in the borrowing andlending rates for the same time period and eliminating the risk offluctuating rates

(3) make variable rate loans with an interest rate tied to some market rate(e.g., 30 day T-bill rate plus a margin), the rate fluctuating with themarket rate but the margin remains fixed. This effectively transforms

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a long term loan into a short term loan in its dependence on interest

rates (as far as the bank is concerned), transferring interest rate riskto the borrower

(4) sell loans in the secondary market (e.g., securitization of mortgages),reducing the bank to the role of a middleman who originates the loanand then funnels the loan payments to the buyer of the loan. It passeson the risk to the buyer of the loan, but also passes on any higherexpected profits to the buyer of the loan as well.

(5) GAP management: classify assets and liabilities by maturity, compar-ing differences or gaps in maturity; decide what mismatch, if any, fora given maturity range is desirable by comparing the profit potential

from the mismatch with the loss potential if rates rise.

12. Why has the failure rate of thrift institutions been high in recent years?

Thrifts have traditionally made long term fixed rate mortgage loans. If aloan is made at a given rate and interest rates subsequently rise, the thriftscost of funds can rise above the rate that it is earning on its loans. If sucha situation occurs for a sustained period, the thrift will inevitably fail.

In addition, poor economic conditions in some regions have caused failuressince smaller banks typically do not diversify loans on a geographic basis. If

hard times fall on a region, there will be widespread default and consequentbank failures.

13. What steps have been taken to reduce the likelihood of bank and thriftfailures in the future?

Five main steps have been taken to reduce the risk of bank failures: (1)capital requirements have been raised, providing a larger cash buffer tothe FDIC, (2) FDIC policy will close institutions sooner, (3) FDIC raisedinsurance premiums to put more funds into the insurance fund, (4) Congresscontributed extra funds (tax payer funds) into the insurance fund, and (5)bank examinations are more stringent.

In addition, there has been discussion but not implementation of (a) riskadjusted insurance premiums on bank deposits requiring high risk banks topay more than low risk banks, (b) a greater geographical diversification ofbanks, and (c) a greater use of market-based valuation of bank assets.

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Chapter 8: Efficient Markets

1. What is an informationally efficient market?

An efficient market is a security market in which all currently available publicinformation is very rapidly reflected in security prices. A market is efficientif a number of investors try to utilize information for their own benefit,since other investors will monitor the flow of information and any beneficialinformation will soon spread throughout the marketplace. The driving forcebehind informational efficiency is simply competition for profits.

2. Describe the economic forces that tend to make financial markets infor-

mationally efficient.

As mentioned in the reponse to problem 1, competition for profits is thedriving force behind informational efficiency. If a security is underpricedgiven the current public information, investors buying the security in antici-pation of price increases will drive the price up to its equilibrium value (Butwho are they buying from? Who wants to sell if the security is undervalued?The fact that the security is underpriced can not be available to everyone,otherwise no one would sell); if a security is overvalued given current publicinformation, investors selling the security in anticipation of price decreasesdrive the price down to its equilibrium value (But who are they selling to?

Who wants to buy if the security is overvalued? The fact that the securityis overvalued can not be available to everyone, otherwise no one would buy).

Tests of market efficiency require the definition of relevant information anda model showing the impact of this information upon prices. These tests ofefficiency are actually joint tests of efficiency and a particular pricing model.

3. Efficiency has sometimes been broken down into weak form, semistrongform, and strong form efficiency. What are the differences between theseforms of efficiency?

The weak form is the basic form of the statement of market efficiency, the

others include additional, stronger requirements. In the weak form state-ment, past price and volume of trading information are instantaneously in-corporated into current prices: knowledge of past price and volume informa-tion adds nothing new and does not allow prediction of future price changes.This means that the expected value for tomorrows price is todays price,

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E(Pt+1) = Pt. An alternative interpretation is in terms of price changes,

that is, E(Pt+1) Pt = 0: the expected price change is zero, price changescan not be predicted in an efficient market.

The semistrong form, in addition to the statements contained in the weakform, states that the impact of nonprice information upon security prices ispractically instantaneous. This means that information about earnings anddividends is rapidly reflected in security prices (stocks), and informationabout determinants of interest rates is instantaneously incorporated intosecurity prices (bonds).

The strong form, in addition to the statements contained in the semistrongform, states that information available to special groups of investors is al-ready incorporated into security prices and is thus of no real value to theseinvestors.

4. Describe the empirical evidence concerning the three forms of the efficientmarket hypothesis.

The weak form is a short run or short term hypothesis covering periods suchas days or perhaps weeks (over long intervals such as years, price changescan and do have up trends and down trends).

The overall evidence is consistent with price changes for commonstocks, bonds, and futures contracts being random.

The evidence is consistent with interest rates following a random walk. Statistically significant patterns in security price changes have not

been found.

Profitable short term trading rules, after subtracting out commissioncosts, have been found to be unprofitable.

These, however, are not compelling pieces of evidence in favor of the efficientmarket hypothesis.

The semistrong form requires a model for the determinants of security prices.Tests of the model must distinguish between anticipated information (which

should already be incorporated in prices) and unanticipated information(which should have the predicted impact on prices).

The existing evidence is consistent with the markets ability to rapidlyreadjust to surprises.

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The accuracy of tests is affected by the procedure for separating an-

nouncements into anticipated components and unanticipated or sur-prise components.

These, too, are not compelling pieces of evidence in favor of the efficientmarket hypothesis. These tests would appear to be far too model dependentto make any far reaching claims based on them.

The strong form addresses three types of special groups of investors: (1)professional money managers, (2) investment advisory services (market let-ters), and (3) corporate insiders (e.g., director, officer, large stockholder,involved in management and having access to information not available tothe public).

(1) professional money managers: the average mutual fund earns fair ratesof returns given the risk levels, which is consistent with efficiency;in addition, the current interest rate is a better forecast of the nextperiods interest rate than the experts forecast.

(2) investment advisory services: following their advice produces no morethan a fair return, consistent with efficiency.

(3) corporate insiders: profits from insider information is illegal for shortterm gains, but for long term investment purposes it is permitted(such insider trading must be reported to the SEC which releases the

information to the public); corporate insiders have done quite well, andsince SEC insider reports have become a source of investor informationavailable to the public, this is not consistent with the strong form.

Concerning corporate insiders, insider profits from mergers and takeovers areillegal, but the price of the acquired firms stock tends to rise significantlyprior to public announcement of a tender offer. In addition, the precisemeaning of insider is subject to judicial interpretation, that is, it is notclear how it should be defined.

There are also a number of efficient market anomalies (5 documented)

which are inconsistent with the efficient market hypothesis:

(1) Weekend Effect: a small, but statistically significant unexplained ten-dency for stock prices to decline over the weekend and on Mondaymornings.

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(2) January Effect: stock returns are relatively high for the month of Jan-

uary, the explanation is not clear but may be due to investors takingtax losses by selling in December (depressing December prices) andpermitting high returns in January (but this would seem to indicatea December Effect as well, that is, relatively low stock returns for themonth of December).

(3) Small Firm Effect: small firms have been found to have relativelyhigh returns after adjusting for risk; this seems to be related to theJanuary Effect since most excess January returns are for small firms;small firms are not carefully monitored by security analysts, resultingin a tendency for good news about small firms to be hidden from themarket; skewness of returns may be an additional factor in this effect.

(4) Individual Investors Performance: some investors have been found tohave abnormally good performance over time (e.g., Value Line Invest-ment Advisory Service which uses a secret mathematical formula todetermine ratings of stocks (from a top rating of 1 to a low ratingof 5), inputting current and past financial data of the correspondingfirms), but evidence is mixed.

(5) Overshooting: security prices for stocks and bonds have been shownto fluctuate more than probable underlying determinants of prices,which may be an indicator of inefficiency or it may be an indicatorof a psychological tendency to put too much weight upon relatively

recent news: (a) the bigger fool theory states that security pricesare determined by whatever people will pay for them, and (b) securityprices are often affected by speculative bubbles, during which bub-bles the price levels are not justified by the objective determinants ofsecurity prices.

5. How should investors behave in a market that is informationally efficient?How does this differ from behavior in a market that is not informationallyefficient?

An investor should decide upon preferences about levels of expected returnsand risk, and select a portfolio accordingly. The investor should minimizetransaction costs and limit the amount of trading since trading costs are notoffset by trading gains in an efficient market. In addition, the investor shouldminimize the amount of taxes paid. On the other hand, the investor should

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not abandon a search for inefficiency in the form of mispriced securities (if

all investors assumed a perfectly efficient market, then the market wouldactually become inefficient - a driving force is required), some investorsmust believe the market to be inefficient in order to drive the market towardefficiency. As for issuers of securities, they should not try to time new issues:long term success in timing is very unlikely since accurate prediction of priceand interest rate changes in the future is not possible in an efficient market.

For an informationally inefficient market, there would be no reason to limittrading since trading gains could become unlimited for a good trader.Taxes would not be a major concern since they could be offset by sufficientlylarge gains. Market timing would become a science for good investors andissuers.

6. What is technical analysis? Why is there a conflict between technicalanalysis and efficient markets?

Technical analysis is the development of predictors of security price changes.A conflict with the efficient market hypothesis arises because any predictiverule using past information should not give an advantage in an efficient mar-ket: any successful rule attracts the attention of profit seeking investors andmarket watchers act as soon as the predictor gives a signal, prices adjustingalmost instantaneously.

A technical analyst must find a predictor that predicts a predictor, and keep

that information secret in order to get a jump on market watchers (perhaps,such as Value Line?). Alternatively, an analyst must find a consistently in-correct predictor and do the opposite to that incorrect predictor (contrarianapproach). For example, the odd lot theory states that odd lot investorsare poorly informed and are consistently incorrect in stock picks: if oddlotters are heavily buying, that is a signal to sell; if odd lotters are heavilyselling, that is a signal to buy. However, the evidence indicates that oddlotters are sometimes correct and sometimes give no signal when one wouldbe expected.

There has been a claim that trading volume statistics can give price changeinformation: high volume on days when prices rise, low volume when prices

drop (bullish signal, sign of rising prices); low volume on days when pricesrise, high volume when prices decline (bearish signal, sign of falling prices).There is, however, no evidence to support a relationship between prices andtrading volume. There does seem to be some evidence relating the absolutesize of price changes and trading volume (heavy trading, large price changes;

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light trading, small price changes), but they may go in opposite directions,

that is, there is no strong correlation in sign.

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Chapter 9: Spot And Forward Interest Rates

1. Assume the following information for spot rates of interest for zero couponbonds and determine the spot prices, forward rates, and forward prices.Graph the yield curve for spot and forward rates.

The spot rates are given in the table below. The spot price, forward rate,and forward price are given by

Dn =1

(1 + Rn)n

fn = (1 + Rn)n

(1 + Rn1)n1 1

Fn =1

(1 + fn)

Consequently, the completed table is:

Maturity Spot Spot Forward Forward(Period) Rate Price Rate Price

1 0.03 0.9709 0.03 0.97092 0.04 0.9246 0.05 0.95243 0.05 0.8638 0.07 0.9174

4 0.06 0.7921 0.09 0.9174

The yield curve for spot and forward rates is simply a plot of the spot rateversus maturity, and a plot of the forward rate versus maturity. The yieldcurve for both spot and forward rates are straight lines, the spot rate yieldcurve has a slope of one with intercept at 0.02; the forward rate yield curvehas a slope of two with intercept at 0.01. The two curves intersect at period1 with a rate of 0.03 (see Figure 9.1).

2. Given the following forward rates, compute the forward prices, spot rates,and spot prices. Graph the spot and forward yield curves.

The forward rates are given in the table below. The forward price, spotprice, and spot rates are given by

Fn =1

(1 + fn)

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Dn = Dn1Fn

Rn = D1/nn 1

where D1 = F1 and R1 = f1. Thus, the completed table is:

Maturity Forward Forward Spot Spot(Period) Rate Price Price Rate

1 0.08 0.9259 0.9259 0.082 0.01 0.9901 0.9167 0.043 0.12 0.8919 0.8185 0.074 0.03 0.9709 0.7947 0.06

The yield curve for both the forward and spot rates are oscillatory or fluc-tuating. The curves intersect three times, once for period 1 at 0.08, oncejust beyond period 2 at approximately 0.05, and once just before period 3at approximately 0.065 (see Figure 9.2).

3. Assume the following information about the prices of STRIPS with $100par values. Compute the spot interest rates, forward interest rates, andforward prices. Graph the spot and forward rates. Assume no taxes.

The spot prices are given in the table below. The spot price, the spot rate,the forward rate, and the forward price are given by

Dn =100

(1 + Rn)n

Rn =

Dn100

1/n 1

fn =(1 + Rn)

n

(1 + Rn1)n1 1

Fn =1

(1 + fn)

where f1 = R1 and F1 = D1. The completed table is thus:

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Maturity Spot Spot Forward Forward

(Period) Price Rate Rate Price1 94.34 0.060 0.060 94.342 88.17 0.065 0.070 93.463 81.64 0.070 0.080 92.594 74.22 0.077 0.098 91.07

The graph of the spot and forward yield curves show that the forward ratealways lies above the spot rate (intersecting at period 1 for a rate of 0.060).Both curves begin to lose their linear appearance as period 4 is approached,the rates being higher than linear extrapolation would give (see Figure 9.3).

4. Given choice of $100 one year from now or $115 two years from now.

Which is better? What does the choice depend upon?

The present value of $100 is D1(100) = 100/(1+ R1) and the present value of$115 is D1(115) = 115/(1 + R2)

2 = 115/(1+ R1)(1+ f1) = 1.15D1(100)/(1 +f1). The choice depends upon the value of the forward rate f1: if 1.15/(1 +f1) > 1 then $115 two years from now is better; on the other hand, if1.15/(1 + f1) < 1 the $100 one year from now is better.

5. Suppose R1 = 0.10, R2 = 0.12, R3 = 0.14, and R4 = 0.16. You are givena choice of $100 at time 1, $110 at time 2, $130 at time 3 and $140 at time4. Compute the time 1 value of each of these cash flows; which is the best?Compute the time 2 cash flows; which is the best? Are the answers to these

questions the same? Why or why not?

The present value (time 0) of each of these cash flows is given by Dn(k) =D(k)/(1+Rn)

n where the time n values are D(1) = 100, D(2) = 110, D(3) =130, and D(4) = 140. The results are D1(1) = 90.91, D1(2) = 87.69, D1(3) =87.75, D1(4) = 77.32. The time 1 values are given by the time 0 valuestimes the forward rate factor (1 + f1) = 1/F1 where forward rate is fn =(1 + Rn)

n/(1 + Rn1)n1 1 = R1 for n = 1. Consequently, the time 1

values are 100, 96.46, 96.525, 85.05. The best is the $100 at time 1. Thetime 2 values are given by the time 1 values times the forward rate factor(1 + f2) = 1/F2 where the forward rate is f2 = 0.140363636. Consequently

the time 2 values are 100, 110, 110.07, 96.99. The best is the $130 at time 3by a few cents. The time 1 and time 2 best values are different is that thetime 1 best value was its maturity value, it does not change from time 1 totime 2 whereas the time 2 best value increases from its time 1 value in orderto reach its time 3 maturity value of $130.

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6. Assume zero coupon bonds with $1 par values. A two period bond has a

price of D2 = 0.70 and a three period bond has a price of D3 = 0.80. Showthe arbitrage opportunities.

Since Dn = 1/(1 + Rn)n, the spot rates corresponding to these prices are

R2 = 0.1952 and R3 = 0.0772 which implies the forward rate from period 2to period 3 is f3 = 0.125: the negative forward rate is an indication thatarbitrage opportunities exist (a different way of stating that D3 > D2 is andindication that arbitrage opportunities exist).

Actions (t=0) 0 1 2 3

Buy 2 period bond 0.70 +1.00Shortsell 3 period bond +0.80 1.00

Net flow = 0.10 +0.10 +1.00 1.00

7. Assume a one period spot rate R1 = 0.10 and a two period spot rateR2 = 0.08. Show how a long forward contract can be created from thesetwo spot bonds and determine the price and yield of the forward contract.Show how a short forward position can be created.

The present values corresponding to the spot rates are D1 = 0.9091 andD2 = 0.8573 and the forward price is F2 = D2/D1 = 0.9431. An investorcan create a long forward contracts (zero cash flow at time 0, cash outflowat time 1, cash inflow at time 2) by buying 2 period bonds and short selling1 period bonds:

Actions (t = 0) 0 1 2

Short sell y 1 period bonds yD1 yBuy x 2 period bonds xD2 +x

Net = x y 0 y +x

where the net position is a long forward. For a forward contract, the netflow at t = 0 must be zero, which imposed the condition that yD1 = xD2 ory = xD2/D1 = xF2 or x = y/F2 and a net forward position of (1 F2)x =(1 F2)y/F2. For a unit outflow at time 1, y = 1, the inflow at time 2 isx = 1.06033 and a net of 0.06033; for a unit inflow at time 2, x = 1, theoutflow at time 1 is y = F2 = 0.9431 and a net of 0.0549.

To create a short forward position (zero cash flow at time 0, cash inflow attime 1, cash outflow at time 2) by buying 1 period bonds and short selling2 period bonds:

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Actions (t = 0) 0 1 2

Short sell y 2 period bonds yD2 yBuy x 1 period bonds xD1 +x

Net = x y 0 +x y

where the net position is a short forward. The zero cash flow condition attime t = 0 imposed the condition that yD2 = xD1 or x = yF2 or y = x/F2and a net short position of (F2 1)y or (F2 1)x/F2. In either case, thisis a sure loss: for a unit outflow at time 2, y = 1, the net is 0.0569; for aunit outflow at time 1, the net is 0.0603. The only way a short forwardposition would prove profitable on its own, is for x > y or F2 > 1 whichimplies a negative value for the forward interest rate f2, indicating that therewould be arbitrage opportunities (the forward rate implicit in R1 and R2 is

different than the market forward rate).

8. Assume D1 = 0.90 and D2 = 0.80. You decide to short a one period zerocoupon bond and go long one two period zero coupon bond. Is the resultingposition a forward position?

Actions (t = 0) 0 1 2

Short sell a 1 period bond 0.9 1Buy a 2 period bond 0.8 +1

Net = +0.1 +0.1 1 +1

This is not a forward position since it involves a non-zero cash flow at time0. This is simply short selling and going long in the spot market for a

guaranteed profit of 0.1.

9. Assume the one period spot rate is R1 = 0.10, the two period spot rateis R2 = 0.08, and the forward rate f2 = 0.0. Is this information consistentwith equilibrium? What arbitrage opportunities are available to investors?

The forward rate implicit in the two spot rates is fim = (1+ R2)2/(1 + R1)

1 = 0.06036, so the market rate for the forward rate is not consistent withequilibrium. An arbitrage opporunity is to borrow at the market forwardrate of 0% and to lend at the 6.036% rate implicit in the spot rates (definethe implicit forward price Fim = 1/(1+fim)): create a short forward positionat the market rate and a long forward position at the rate implicit in the

spot rates.Action (t = 0) 0 1 2

Short forward at market f2 rate 0 +1 1Go long forward at implicit f2 rate 0 Fim +1

Net = fimFim 0 1 Fim 0

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where the net position is an arbitrage position. For the numerical values

supplied, this is a riskless profit of 0.059797.

10. Assume R1 = 0.12, R2 = 0.10, and R3 = 0.03. Are these interest ratesconsistent with equilibrium? Explain why or why not.

The spot rates corresponding to these spot rates are D1 = 0.89286, D2 =0.82645, and D3 = 0.91514. Equilibrium requires Dj > Dj+1 for all j,and since D3 > D1 > D2, these rates are not consistent with equilibrium.The equilibrium inequality constraint on the spot prices tranlates into spotrate inequality Rn > (1 + Rn1)

(n1)/n 1. For the stated value of R1,R3 > 0.03895; for the stated value of R2, R3 > 0.0656.

11. Assume D2 = 0.85 and D4 = 0.75. What statements can be made aboutf3 and f4? What are the largest possible values for these forward rates?

Since the forward rate is given by 1 +fm = 1/Fm = Dm1/Dm, using m = nand m = n 1 and multiplying together gives

(1 + fn)(1 + fn1) =

Dn1

Dn

Dn2Dn1

=

Dn2Dn

Thus, the forward rates are given by

fn =

Dn2Dn 1

fn1

(1 + fn1)

fn1 =

Dn2Dn

1 fn

(1 + fn)

Since the forward rates are required to be positive, these equations showthat fn Dn2/Dn 1 and fn1 Dn2/Dn 1. The maximum value forf3 occurs for f4 = 0 (D3 = D4) or (f3)max = Dn2/Dn 1 = 1.13333; themaximum value for f4 occurs for f3 = 0 (D2 = D3) or (f4)max = 1.133333.

12. Obtain prices and yields of U.S. Treasury STRIPS fromThe Wall Street

Journal. Plot the yields to maturity versus maturity at yearly intervals.

13. Given the following information about forward interest rates, what isthe smallest possible value of the four period spot interest rate and what will

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the forward interest rate be? What is the largest possible value for the four

period spot interest rate and what will the forward rate be? See AppendixB.

Maturity (n) Forward Rate (fn) Time Interval

1 0.12 from t = 0 to t = 12 0.10 from t = 1 to t = 23 0.08 from t = 2 to t = 3

Since the relation between the spot rates and the forward rate is (1+Rn)n =

(1+Rn1n1)(1+fn), and since the forward rates are positive, fn 0, Rn (1+

Rn1)(n1)/n. Using the forward rates to generate the spot rates (R1 = f1),

we obtain the following table:

Maturity (n) Forward Rate (fn) Spot Rate (Rn)1 0.12 0.122 0.10 0.113 0.08 0.10

Consequently, R4 (1+R3)0.75. The minimum value occurs for the equality

(R4)min = (1 + R3)0.75 = 0.074 and corresponds to a zero forward rate,

f4 = 0.0: these are the smallest possible values for the four period rates,those rates which make D4 = D3.

As far as maximum values are concerned, there doesnt seem to be any wayto determined these values with the information given. The upper boundsare determined by the five period rates: given a minimum four period spotrate, we can calculate a minimum five period spot rate corresponding to azero five period forward rate, but this is not the maximum four period spotrate. The lower period rates can determine minimum values for the nextperiod rates, but they can not determine the maximum values.

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Chapter 10: Coupon Bearing Bonds

1. Compute the present value of a two period annuity of $1 per period ifthe discount rate is 10%.

The present value of an annuity paying $1 per period for n periods is

An =n

k=1

1

(1 + R)k=

1

R

1 +

1

(1 + R)n

where R is the discount rate. For n = 2 and R = 0.10, the two periodannuity has a present value of A2 = 1.7355.

2. A 2 period annuity has a present value of $1.808. Find the discount ratefrom the present value table.

Looking up the present value in the annuity tables, one finds that the dis-count rate is 7%. An iterative procedure can be set up to solve this numer-ically by writing

R(k + 1) =1

A2

1 1

(1 + R(k))2

where k is the iteration index and an initial value R(0) must be assumed.The rapidity of convergence of the iteration will depend on this initial choice.For instance, choosing R(0) = 1/A2 = 0.5531 leads to convergence relativelyslowly, but lucky guesses close to the correct value will convergence fairlyrapidly. An alternative interative procedure is

R(k + 1) =1

(1 A2R(k))1/2 1

but this has no obvious advantages over the first method and it has a poten-tial disadvantage in that it may lead to unphysical complex values duringthe iterative procedure if R(0) is chosen to be too large.

3. The one period spot rate is R1 = 0.04, the two period spot rate interestrate is R2 = 0.10. Compute the present value of a two period annuity.Approximate the yield to maturity on this annuity. How does this yield tomaturity compare to the one period spot rate and the two period spot rate?

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The present value of a general n period annuity that pays $1 per period is

An =n

k=1

1

(1 + Rk)k

For the two period case this is simply A2 = (1 + R1)1 + (1 + R2)

2. Sub-stituting the values for the spot rate, we obtain A2 = 1.78798. The yield tomaturity is the flat rate that solves the equation

A2 =1

y

1 +

1

(1 + y)2

Using the approximate formula given in the text for maturities of less than15 years, y = 2(1 A2/2)/A2 = 0.1186 which is not a good approximation(it corresponds to a present value of 1.69317, an error of 5%). An iterativeprocedure solution defined by

y(k + 1) =1

A2

1 +

1

(1 + y(k))2

with y(0)

"money and capital markets" by miles livingston: a solution and study manual

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