calculation of hpy and risks of investment

Why Do Individuals Invest ?

By saving money (instead of spending it), individuals tradeoff present consumption for a larger future consumption.

04.1$%400.1$

How Do We Measure The Rate Of Return On An Investment ?

The pure rate of interest is the exchange rate between future consumption and present consumption. Market forces determine this rate.

People’s willingness to pay the difference for borrowing today and their desire to receive a surplus on their savings give rise to an interest rate referred to as the pure time value of money.


If the future payment will be diminished in value because of inflation, then the investor will demand an interest rate higher than the pure time value of money to also cover the expected inflation expense.


If the future payment from the investment is not certain, the investor will demand an interest rate that exceeds the pure time value of money plus the inflation rate to provide a risk premium to cover the investment risk.


Defining an InvestmentA current commitment of Tk. for a period of time in order to derive future payments that will compensate for:– the time the funds are committed– the expected rate of inflation– uncertainty of future flow of

funds.

Measures of Historical Rates of Return

Holding Period Return

10.1 $200

$220

Investment of Value Beginning

Investment of Value EndingHPR

1.1


Holding Period Yield

HPY = HPR - 1

1.10 - 1 = 0.10 = 10%

1.2

Annual Holding Period ReturnAnnual HPR = HPR 1/n

where n = number of years investment is held

Annual Holding Period YieldAnnual HPY = Annual HPR - 1



Arithmetic Mean

yields period holding annual of sum the HPY

:whereHPY/AM

n

A Portfolio of Investments

The mean historical rate of return for a portfolio of investments is measured as the weighted average of the HPYs for the individual investments in the portfolio.

Computation of HoldingPeriod Yield for a Portfolio

# Begin Beginning Ending Ending Market Wtd.Stock Shares Price Mkt. Value Price Mkt. Value HPR HPY Wt. HPY

A 100,000 10$ 1,000,000$ 12$ 1,200,000$ 1.20 20% 0.05 0.010 B 200,000 20$ 4,000,000$ 21$ 4,200,000$ 1.05 5% 0.20 0.010 C 500,000 30$ 15,000,000$ 33$ 16,500,000$ 1.10 10% 0.75 0.075

Total 20,000,000$ 21,900,000$ 0.095

21,900,000$ 20,000,000$

HPY = 1.095 - 1 = 0.095

= 9.5%

HPR = = 1.095

Definition of Risk

1. Uncertainty of future outcomes

or

2. Probability of an adverse outcome

Risk Aversion

Given a choice between two assets with equal rates of return, most investors will select the asset with the lower level of risk.

Not all investors are risk averse

Risk preference may have to do with amount of money involved - risking small amounts, but insuring large losses

Markowitz Portfolio Theory

• Quantifies risk• Derives the expected rate of return for a

portfolio of assets and an expected risk measure• Shows that the variance of the rate of return is a

meaningful measure of portfolio risk• Derives the formula for computing the variance

of a portfolio, showing how to effectively diversify a portfolio

Assumptions of Markowitz Portfolio Theory

1. Investors consider each investment alternative as being presented by a probability distribution of expected returns over some holding period.


2. Investors minimize one-period expected utility, and their utility curves demonstrate diminishing marginal utility of wealth.


3. Investors estimate the risk of the portfolio on the basis of the variability of expected returns.


4. Investors base decisions solely on expected return and risk, so their utility curves are a function of expected return and the expected variance (or standard deviation) of returns only.


5. For a given risk level, investors prefer higher returns to lower returns. Similarly, for a given level of expected returns, investors prefer less risk to more risk.

Markowitz Portfolio Theory

Using these five assumptions, a single asset or portfolio of assets is considered to be efficient if no other asset or portfolio of assets offers higher expected return with the same (or lower) risk, or lower risk with the same (or higher) expected return.

Alternative Measures of Risk

• Variance or standard deviation of expected return

• Range of returns• Returns below expectations

– Semivariance – a measure that only considers deviations below the mean

– These measures of risk implicitly assume that investors want to minimize the damage from returns less than some target rate

Expected Rates of Return

• For an individual asset - sum of the potential returns multiplied with the corresponding probability of the returns

• For a portfolio of assets - weighted average of the expected rates of return for the individual investments in the portfolio

Risk Aversion

The assumption that most investors will choose the least risky alternative, all else being equal and that they will not accept additional risk unless they are compensated in the form of higher return

Expected Rates of Return

n

i 1

i

Return) (Possible Return) ofy Probabilit(

)E(R Return Expected

)R(P....))(R(P))(R[(P nn2211

))(RP(1

ii

n

i

1.6

Measuring the Risk of Expected Rates of Return

2n

1i

Return) Expected-Return (Possibley)Probabilit(

)( Variance

2iii

1

)]E(R)[RP(

n

i

Measuring the Risk of Expected Rates of ReturnStandard Deviation is the square

root of the variance

Computation of Expected Return for an Individual Risky Investment

0.25 0.08 0.02000.25 0.10 0.02500.25 0.12 0.03000.25 0.14 0.0350

E(R) = 0.1100

Expected Return(Percent)Probability

Possible Rate ofReturn (Percent)

Exhibit 7.1

Variance (Standard Deviation) of Returns for an Individual Investment

Possible Rate Expected

of Return (Ri) Return E(Ri) Ri - E(Ri) [Ri - E(Ri)]2 Pi [Ri - E(Ri)]

2Pi

0.08 0.11 0.03 0.0009 0.25 0.0002250.10 0.11 0.01 0.0001 0.25 0.0000250.12 0.11 0.01 0.0001 0.25 0.0000250.14 0.11 0.03 0.0009 0.25 0.000225

0.000500

Exhibit 7.3

Variance ( 2) = .00050

Standard Deviation ( ) = .02236

Measuring the Risk of expected Rates of Return

A relative measure of risk, in some cases, an unadjusted variance or standard deviation can be misleading. If conditions for two or more investment alternatives are not similar- that is, if there are major differences in the expected rates of return- it is necessary to use a measure of relative variability to indicate risk per unit of expected return. A widely used relative measure of risk is the coefficient of variation (CV) calculated in the following slide.

Measuring the Risk of Expected Rates of Return

Coefficient of variation (CV) a measure of relative variability that indicates risk per unit of return

Standard Deviation of ReturnsExpected Rate of Returns

E(R)i

Determinants of Required Rates of Return

• Time value of money

• Expected rate of inflation

• Risk involved

The Real Risk Free Rate (RRFR)

–Assumes no inflation.–Assumes no uncertainty about future

cash flows.–Influenced by time preference for

consumption of income and investment opportunities in the economy

Adjusting For InflationReal RFR =

1Inflation) of Rate(1

RFR) Nominal1(

Nominal Risk-Free Rate

Dependent upon– Conditions in the Capital Markets

– Expected Rate of Inflation

Adjusting For Inflation

Nominal RFR = (1+Real RFR) x (1+Expected Rate of Inflation) -

1

Facets of Fundamental Risk

• Business risk

• Financial risk

• Liquidity risk

• Exchange rate risk

• Country risk

Business Risk

• Uncertainty of income flows caused by the nature of a firm’s business

• Sales volatility and operating leverage determine the level of business risk.

Financial Risk• Uncertainty caused by the use of debt

financing.• Borrowing requires fixed payments which

must be paid ahead of payments to stockholders.

• The use of debt increases uncertainty of stockholder income and causes an increase in the stock’s risk premium.

Liquidity Risk• Uncertainty is introduced by the secondary

market for an investment.– How long will it take to convert an investment

into cash?

– How certain is the price that will be received?

Exchange Rate Risk

• Uncertainty of return is introduced by acquiring securities denominated in a currency different from that of the investor.

• Changes in exchange rates affect the investors return when converting an investment back into the “home” currency.

Country Risk• Political risk is the uncertainty of returns

caused by the possibility of a major change in the political or economic environment in a country.

• Individuals who invest in countries that have unstable political-economic systems must include a country risk-premium when determining their required rate of return

Risk Premium

f (Business Risk, Financial Risk, Liquidity Risk, Exchange Rate Risk, Country Risk)

orf (Systematic Market Risk)

Risk Premium and Portfolio Theory

• The relevant risk measure for an individual asset is its co-movement with the market portfolio

• Systematic risk relates the variance of the investment to the variance of the market

• Beta measures this systematic risk of an asset

Fundamental Risk versus Systematic Risk

• Fundamental risk comprises business risk, financial risk, liquidity risk, exchange rate risk, and country risk

• Systematic risk refers to the portion of an individual asset’s total variance attributable to the variability of the total market portfolio

Relationship BetweenRisk and Return

Rateof Return

Risk(business risk, etc., or systematic risk-beta)

RFR

SecurityMarket LineLow

RiskAverageRisk

HighRisk

The slope indicates therequired return per unit of risk

(Expected)

Changes in the Required Rate of Return Due to Movements Along the SML

Rate

Risk(business risk, etc., or systematic risk-beta)

RFR

SecurityMarket Line

Expected

Movements along the curvethat reflect changes in therisk of the asset

Changes in the Slope of the SML

RPi = E(Ri) - NRFR

where:

RPi = risk premium for asset i

E(Ri) = the expected return for asset i

NRFR = the nominal return on a risk-free asset

Market Portfolio RiskThe market risk premium for the market portfolio (contains all the risky assets in the market) can be computed:

RPm = E(Rm)- NRFR where:

RPm = risk premium on the market portfolio

E(Rm) = expected return on the market portfolio

NRFR = expected return on a risk-free asset

Change in Market Risk Premium

Risk

RFR

Original SML

New SML

Rm

Rm'

E(R)

NRFR

Expected Return

Rm´

Rm

Capital Market Conditions, Expected Inflation, and the SML

Risk

RFR

Original SML

New SMLRate of Return

RFR'

NRFR

NRFR´

Expected Return

Variance (Standard Deviation) of Returns for an Individual Investment

Standard deviation is the square root of the variance

Variance is a measure of the variation of possible rates of return Ri, from the expected rate of return [E(Ri)]

Covariance of Returns

• A measure of the degree to which two variables “move together” relative to their individual mean values over time