RETURN DAN RISIKO

Puput Tri Komalasari

Defining ReturnDefining ReturnDefining ReturnDefining Return

Income received Income received on an investment plus on an investment plus any any change in market pricechange in market price, usually , usually

expressed as a percent of the expressed as a percent of the beginning market price beginning market price of the of the

investment.investment.

Income received Income received on an investment plus on an investment plus any any change in market pricechange in market price, usually , usually

expressed as a percent of the expressed as a percent of the beginning market price beginning market price of the of the

investment.investment.

Sources of Investment Sources of Investment ReturnsReturns

Investments provide two basic types of Investments provide two basic types of return:return:

Income returns(yield)Income returns(yield) The owner of an investment has the right to any The owner of an investment has the right to any

cash flows paid by the investment.cash flows paid by the investment. Changes in price or value (capital gain/loss)Changes in price or value (capital gain/loss)

The owner of an investment receives the benefit The owner of an investment receives the benefit of increases in value and bears the risk for any of increases in value and bears the risk for any decreases in value.decreases in value.

Total Return =Yield +Price ChangeTotal Return =Yield +Price Change

Income ReturnsIncome Returns

Cash payments, Cash payments, usually received usually received regularly over the regularly over the life of the life of the investment.investment.

Examples: Coupon Examples: Coupon interest payments interest payments from bonds, from bonds, Common and Common and preferred stock preferred stock dividend payments.dividend payments.

Returns From Changes Returns From Changes in Valuein Value

Investors also Investors also experience capital experience capital gains or losses as the gains or losses as the value of their value of their investment changes investment changes over time.over time.

For example, a stock For example, a stock may pay a $1 dividend may pay a $1 dividend while its value falls while its value falls from $30 to $25 over from $30 to $25 over the same time period.the same time period.

Measuring ReturnsMeasuring Returns Dollar ReturnsDollar Returns

How much money was made on an investment How much money was made on an investment over some period of time?over some period of time?

Total Dollar Return = Income + Price ChangeTotal Dollar Return = Income + Price Change Holding Period ReturnHolding Period Return

By dividing the Total Dollar Return by the By dividing the Total Dollar Return by the Purchase Price (or Beginning Price), we can Purchase Price (or Beginning Price), we can better gauge a return by incorporating the better gauge a return by incorporating the size of the investment made in order to get the size of the investment made in order to get the dollar return.dollar return.

Risk and Risk Premiums

P

DPPHPR0

101

HPR = Holding Period Return

P0 = Beginning price

P1 = Ending price

D1 = Dividend during period one

Rates of Return: Single Period

Return = Capital gain (loss) + yield

Return ExampleReturn Example

The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share, and

shareholders just received a $1 dividend. What return was earned over the past year?

The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share, and

shareholders just received a $1 dividend. What return was earned over the past year?

$1.00$1.00 + ($9.50$9.50 - $10.00$10.00 )$10.00$10.00RR = = 5%5%

For a Treasury security, what is For a Treasury security, what is the required rate of return?the required rate of return?

RequiredRequired

rate of rate of

returnreturn==

RequiredRequired

rate of rate of

returnreturn==

Risk-freeRisk-freerate ofrate ofreturnreturn

For a Treasury security, what is For a Treasury security, what is the required rate of return?the required rate of return?

Since Treasury’s are essentially Since Treasury’s are essentially free of free of default riskdefault risk, the rate of return on a , the rate of return on a Treasury security is considered the Treasury security is considered the

“risk-free”“risk-free” rate of return. rate of return.

RequiredRequired

rate of rate of

returnreturn==

For a For a corporate stock or bondcorporate stock or bond, what is , what is the required rate of return?the required rate of return?

RequiredRequired

rate of rate of

returnreturn==

Risk-freeRisk-freerate ofrate ofreturnreturn

For a For a corporate stock or bondcorporate stock or bond, what is , what is the required rate of return?the required rate of return?

RequiredRequired

rate of rate of

returnreturn==

Risk-freeRisk-freerate ofrate ofreturnreturn

++RiskRisk

PremiumPremium

For a For a corporate stock or bondcorporate stock or bond, what is , what is the required rate of return?the required rate of return?

How large of a risk premium How large of a risk premium should we require to buy a should we require to buy a

corporate security? corporate security?

ReturnsReturns

Expected ReturnExpected Return - the return - the return that an investor expects to that an investor expects to earn on an asset, given its earn on an asset, given its price, growth potential, etc.price, growth potential, etc.

Realized ReturnRealized Return - the return - the return that actually received or that actually received or earned by investor.earned by investor.

Determining Realized ReturnDetermining Realized Return

Total ReturnTotal Return Relative ReturnRelative Return Adjusted ReturnAdjusted Return

Determining Average ReturnDetermining Average Return Arithmetic Arithmetic

ReturnReturn Geometric Geometric

ReturnReturn

RELATIVE RETURN

Relative Return = Total Return + 1

DDtt + (PPtt - P - Pt-1t-1 )

PPt-1t-1

Relative Return = + 1

DDtt + PPtt

PPt-1t-1

Relative Return =

ADJUSTED RETURN

Return adjusted by inflation

(1 + R 1 + R )

(1 + IF)(1 + IF)RIA = - 1

INFLATION-INTEREST RATE RELATIONSHIP

• Factors Influencing Rates:1. Supply

o Households

2. Demand

o Businesses

3. Government’s Net Supply and/or Demand

o Federal Reserve Actions

Real and Nominal Rates of Interest Nominal interest rate Growth rate of your money

Real interest rate Growth rate of your purchasing power

If R is the nominal rate and r the real rate and i is the inflation rate (fisher effect):

Example: r = 3%, i = 6%R = 9% = 3% + 6% or r = 9% - 6% = 3%

Fisher effect: Exactr = (R - i) / (1 + i) = (9%-6%) / (1.06) = 2.83%

r R i

Equilibrium Real Rate of Interest

Determined by: Supply Demand Government actions Expected rate of inflation

Figure 5.1 Determination of the Equilibrium Real Rate of Interest

Equilibrium Nominal Rate of Interest As the inflation rate increases,

investors will demand higher nominal rates of return

If E(i) denotes current expectations of inflation, then we get the Fisher Equation:

( )R r E i

Taxes and the Real Rate of Interest

Tax liabilities are based on nominal income

Given a tax rate (t), nominal interest rate (R), after-tax interest rate is R(1-t)

Real after-tax rate is:

(1 ) ( )(1 ) (1 )R t i r i t i r t it

Annualized Returns

• If we have return or income/price change information over a time period in excess of one year, we usually want to annualize the rate of return in order to facilitate comparisons with other investment returns. We typically express all investment as an effective annual rate (EAR)

Examples:

Suppose prices of zero coupon bond treasuries with $100 face value and various maturities are as follows:

Horizon, T

Price Total Return

Risk-Free Return for Given Horizon

EAR

Half-year

$97.36(100/97.36) – 1

0.0271

2.71% 5.49%

1 year $95.52(100/95.52) – 1

0.0469

4.69% ?

25 years $23.30(100/23.30) – 1

3.2918

329.18% 6.0% Tf TrEAR /1)(11

ANNUAL PERCENTAGE RATES

Rates on short-term investments (T<1 year) often are annualized using simple rather than compound interest.

APR = n x rf(T)

Measuring Historic Returns Starting with annualized Holding

Period Returns, we often want to calculate some measure of the “average” return over time on an investment.

Two commonly used measures of average: Arithmetic Mean Geometric Mean

Arithmetic Mean Return The arithmetic mean is the “simple

average” of a series of returns. Calculated by summing all of the

returns in the series and dividing by the number of values.

RA = (HPR)/n Oddly enough, earning the arithmetic

mean return for n years is not generally equivalent to the actual amount of money earned by the investment over all n time periods.

Arithmetic Mean Example

Year Holding Period Return 1 10% 2 30% 3 -20% 4 0% 5 20%

RA = (HPR)/n = 40/5 = 8%

Geometric Mean Return

The geometric mean is the one return that, if earned in each of the n years of an investment’s life, gives the same total dollar result as the actual investment.

It is calculated as the nth root of the product of all of the n return relatives of the investment.

RG = [(Return Relatives)]1/n – 1

Geometric Mean Example

Year Holding Period Return Return Relative

1 10% 1.10 2 30% 1.30 3 -20% 0.80 4 0% 1.00 5 20% 1.20

RG = [(1.10)(1.30)(.80)(1.00)(1.20)]1/5 – 1

RG = .0654 or 6.54%

Arithmetic vs. Geometric

To ponder which is the superior measure, consider the same example with a $1000 initial investment. How much would be accumulated?

Year Holding Period Return Investment Value

1 10% $1,100 2 30% $1,430 3 -20% $1,144 4 0%$1,144 5 20% $1,373

Arithmetic vs. Geometric

How much would be accumulated if you earned the arithmetic mean over the same time period?

Value = $1,000 (1.08)5 = $1,469 How much would be accumulated if you

earned the geometric mean over the same time period?

Value = $1,000 (1.0654)5 = $1,373 Notice that only the geometric mean

gives the same return as the underlying series of returns.

Determining Expected Return (Discrete Dist.)Determining Expected Return (Discrete Dist.)

R = ( Ri )( Pi )

R is the expected return for the asset,

Ri is the return for the ith possibility,

Pi is the probability of that return occurring,

n is the total number of possibilities.

R = ( Ri )( Pi )

R is the expected return for the asset,

Ri is the return for the ith possibility,

Pi is the probability of that return occurring,

n is the total number of possibilities.

n

i=1

Expected ReturnExpected Return

State of Probability Return

Economy (P) Comp. A Comp. B

Recession .20 4% -10%

Normal .50 10% 14%

Boom .30 14% 30%

For each firm, the expected return on the stock is just a weighted average:

Expected ReturnExpected Return

State of Probability Return

Economy (P) Comp. A Comp. B

Recession .20 4% -10%

Normal .50 10% 14%

Boom .30 14% 30%

For each firm, the expected return on the stock is just a weighted average:

R = P1*R1 + P2*R2 + ...+ Pn*Rn

Expected ReturnExpected Return

State of Probability Return

Economy (P) Comp. A Comp. B

Recession .20 4% -10%

Normal .50 10% 14%

Boom .30 14% 30%

R = P1*R1 + P2*R2 + ...+ Pn*Rn

RA = .2 (4%) + .5 (10%) + .3 (14%) = 10%

Expected ReturnExpected Return

State of Probability Return

Economy (P) Comp. A Comp. B

Recession .20 4% -10%

Normal .50 10% 14%

Boom .30 14% 30%

R = P1*R1 + P2*R2 + ...+ Pn*Rn

RB = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%

Based only on your expected return

calculations, which stock would you

prefer?

RISK?RISK?

Have you considered

Defining RiskDefining Risk

What rate of return do you expect on your investment (savings) this year?

What rate will you actually earn?

Does it matter if it is a bank CD or a share of stock?

What rate of return do you expect on your investment (savings) this year?

What rate will you actually earn?

Does it matter if it is a bank CD or a share of stock?

The variability of returns from The variability of returns from those that are expected.those that are expected.

The variability of returns from The variability of returns from those that are expected.those that are expected.

Defining Risk• The possibility that an actual return

will differ from our expected return.

• Uncertainty in the distribution of possible outcomes.

What is Risk?What is Risk?• Uncertainty in the distribution of

possible outcomes.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

4 8 12

Company A

return

What is Risk?What is Risk?• Uncertainty in the distribution of

possible outcomes.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

-10 -5 0 5 10 15 20 25 30

Company B

return

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

4 8 12

Company A

return

What is risk?What is risk?

Risk is the uncertainty associated with the Risk is the uncertainty associated with the return on an investment.return on an investment.

Risk can impact all components of return Risk can impact all components of return through:through: Fluctuations in income returns;Fluctuations in income returns; Fluctuations in price changes of the Fluctuations in price changes of the

investment;investment; Fluctuations in reinvestment rates of return.Fluctuations in reinvestment rates of return.

6-46

• Financial Risk– Tied to debt financing

• Liquidity Risk– Marketability with-out

sale prices

• Exchange Rate Risk• Country Risk

– Political stability

Risk Sources

• Interest Rate Risk– Affects income return

• Market Risk– Overall market effects

• Inflation Risk– Purchasing power

variability

• Business Risk

6-47

Risk Types

• Two general types:– Systematic (general) risk

• Pervasive, affecting all securities, cannot be avoided

• Interest rate or market or inflation risks

– Nonsystematic (specific) risk• Unique characteristics specific to issuer

• Total Risk = General Risk + Specific Risk

How do we Measure Risk?How do we Measure Risk?

• To get a general idea of a stock’s price variability, we could look at the stock’s price range over the past year.

How do we Measure Risk?How do we Measure Risk?

• A more scientific approach is to examine the stock’s STANDARD DEVIATION of returns.

• Standard deviation is a measure of the dispersion of possible outcomes.

• The greater the standard deviation, the greater the uncertainty, and therefore , the greater the RISK.

Standard DeviationStandard Deviation

n

i=1

= (Ri - R)2 × Pi

Which stock would you prefer?

How would you decide?

Which stock would you prefer?

How would you decide?

Company

Company A B

Expected Return 10% 14%

Standard Deviation 3.46% 13.86%

Company

Company A B

Expected Return 10% 14%

Standard Deviation 3.46% 13.86%

SummarySummarySummarySummary

It depends on your tolerance for risk! It depends on your tolerance for risk!

It depends on your tolerance for risk! It depends on your tolerance for risk!

Remember there’s a tradeoff between risk and return.Remember there’s a tradeoff between risk and return.

Return

Risk

Determining Expected Return (Continuous Dist.)Determining Expected Return (Continuous Dist.)

R = ( Ri ) / ( n )

R is the expected return for the asset,

Ri is the return for the ith observation,

n is the total number of observations.

R = ( Ri ) / ( n )

R is the expected return for the asset,

Ri is the return for the ith observation,

n is the total number of observations.

n

i=1

Determining Standard Deviation (Risk Measure)Determining Standard Deviation (Risk Measure)

n

i=1 = ( Ri - R )2

( n )

Note, this is for a continuous distribution where the distribution is for a population. R represents

the population mean in this example.

= ( Ri - R )2

( n )

Note, this is for a continuous distribution where the distribution is for a population. R represents

the population mean in this example.

Coefficient of Variation

• The coefficient of variation is the ratio of the standard deviation divided by the return on the investment; it is a measure of risk per unit of return.

CV = /RA

• The higher the coefficient of variation, the riskier the investment.