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Investments:Risk and Return

Business Administration 365

Professor Scott Hoover

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Returns Return measure of the benefit received from an

investment

holding period return % change in value over the period

effective annual return (EAR) 1-year holding period return includes the effects of compounding.

annual percentage rate (APR) per period rate × # of periods per year ignores the effects of compounding

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If rp is the per period rate and m is the # of compounding periods per year,

Putting those together gives

The distinction is important because… Annual discount rates must be EARs Banks quote APRs Bond yield-to-maturities (YTMs) are APRs Credit cards and option valuation models use continuously-

compounded interest rates APRs with m = ∞

1-)(1EAR

APRm

p

p

r

rm

1-1EARm

m

APR

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A few examples… A bank quotes 9% APR, compounded monthly.

Per period rate 9%/12 = 0.75% EAR = 1.007512 - 1 = 9.38%

A bond pays 4% interest every six months. YTM = 4%×2 = 8% EAR = 1.042 - 1 = 8.16%

The continuously-compounded interest rate is 6% per year. What happens as m gets bigger?

m = 10 → EAR = 6.165% m = 100 → EAR = 6.182% m = 1000 → EAR = 6.183% m = ∞ → EAR = 6.184%

11-1EAR lim

APRm

m

em

APR

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Risk Risk measure of the potential for loss in an

investment How should we measure risk?

Reality: we really don’t know how to best measure risk.

What do we know about risk? Some risk is all but eliminated in well-diversified

portfolios diversifiable risk (aka, idiosyncratic risk, firm-specific

risk) Some risk remains no matter how well-diversified we are

non-diversifiable risk (aka, systematic risk, market risk)

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Capital Asset Pricing Model (CAPM) Intuition: Investors will only be compensated for the level

of non-diversifiable risk they take on. Why? Definition: market portfolio ≡ portfolio of all assets

weighted according to their market values. Result

Expected return on a well-diversified portfolio is a linear function of the standard deviation of the portfolio’s returns Why is std. dev. a reasonable measure here?

The line is called the Capital Market Line (CML) E(R) = Rf + (/ m)(E(Rm)-Rf) R return on portfolio Rm return on market portfolio Rf risk-free return std. dev. of portfolio m std. dev. of market portfolio

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Risk (standard deviation)

Expected Return

m

E(Rm)

Rf

Capital Market Line

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The CML is useful for well-diversified portfolios, but not for individual assets.

To eliminate diversifiable risk, we extract the portion of the standard deviation that is correlated with the market. This leaves , which is our measure of the non-diversifiable risk

of an asset.

≡ correlation between asset returns and market returns Result: expected return on any asset is a linear function of This line is called the Security Market Line (SML)

E(R) = Rf + (E(Rm)-Rf)

mm

m

m

m

RVAR

RRCOV

2

,

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Risk (beta)

Expected Return

E(Rm)

Rf

Security Market Line

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Roughly speaking, beta tells us how the asset price tends to move when the market moves. e.g., Suppose =1.5 for some asset. The asset will tend

to move by 15% whenever the market moves by 10%.

Do assets with negative betas exist? After all, E(R) < Rf

Yes! Such assets provide insurance on the portfolio

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Miscellaneous Notes If markets are efficient, investing is nothing more than choosing a

and a method to achieve it. invest in a combination of the risk-free and a market index

Portfolio betas The beta of a portfolio is the weighted average of the betas of

the individual assets in the portfolio:

p = wAA + wBB + …

The weights are the fraction of our money we have invested in each, with short positions having negative weights

example: Suppose we have $10,000 to invest and that we short $6,000 of one asset. We then invest $16,000 into a second asset.

w1 = -$6,000/$10,000 = -0.6w2 = $16,000/$10,000 = 1.6

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Problems with using the CAPM What is the market portfolio?

can include every conceivable asset (stocks, bonds, baseball cards, ostrich eggs, etc.).

difficult to measure, so we proxy by using a market index (such as the S&P500 or the Russell 3000).

expected return on the market portfolio is difficult to estimate. def’n: market risk premium (MRP) = E(Rm)-Rf

One study shows that the MRP was about 7.4% from 1926-1999.

Recent evidence suggests that it should be around 4%.

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Other factors may be important. Historical returns may not be representative of future

returns. See spreadsheet example

What if we don’t have historical data for the asset? find comparables use common sense

Bottom Line: use the CAPM and common sense to estimate the appropriate discount rate

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Applying the CAPM gives the appropriate rate for discounting cash

flows to shareholders used as part of the WACC calculation

WACC = wdRd(1-T) + wpsRps + weRe

Recall that wi fraction of firm (using mkt values) financed with type i T tax rate Re required return on equity

estimated using CAPM Rps required return on preferred stock

estimated using D/P Rd required return on debt

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Techniques to estimate cost of debt #1: Find the yield-to-maturity on the company’s

outstanding debt Potential problems

1. YTM depends on the maturity of the debt.If the company’s debt has a very long or very short maturity, our estimate may be biased.

2. The YTM does not reflect the expected return to investors.

3. The company’s debt may not be publicly-traded 4. Bonds with embedded options are problematic.

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#2: Use the company’s debt rating in conjunction with yield spreads to estimate the company’s cost of debt. yield spread: the difference between the yield on a bond (or

class of bonds) and a corresponding Treasury bond with the same maturity

example: Suppose a company’s debt is rated Baa1 by Moody’s. What is our best estimate of the company’s cost of debt? Suppose we choose to use a ten-year maturity for our

estimates. From www.bondsonline.com, we see that the yield

spread is 107 basis points, or 1.07%. (Note that this is an old estimate).

From www.cnnfn.com, we see that ten-year Treasuries have a yield of 3.89%

Cost of debt estimate = 3.89%+1.07% = 4.96%

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Potential problems The company’s debt may not be rated The bond may not be an average bond within its ratings

class.

#3: Find the cost of debt on comparable companies