Risk and ReturnChapter 4

High Return Comes Only with High Risk

Measuring Return Holding Period Return Annual Return

› Current Yield + Capital Gains Current Yield = Cash Received During

The Year/Initial Price Capital Gains = (Year-end Price – Initial

Price)/Initial Price

Average Return Arithmetic Average Return = k = 1/n ∑ kt Year Return 2005 20 % 2006 22% 2007 18% 2008 26% 2009 21% 2010 16% 2011 17%Sum of Returns = 140 Arithmetic Average = 140/7 = 20

Geometric Average Return Geometric Return: (1+ it)1/n -1 [1.2x1.22x1.18x1.26x1.21x1.16x1.17]1/

7 -1 =

3.574562 1/7 -1 = 1.199587- 1 = .1996 or 19.96%.

For positive returns, Geometric Average is always less than arithmetic average

Expected Return When we are dealing with future, we

assign probabilities to future returns. The probability adjusted average is expected return

E(k) = ∑ kipi

Calculation of Expected Return

Economic Scenario Return(ki) Prob (pi) kipi Recession -5% .25 -1.25 Normal 18% .50 9 Boom 35% .25 8.75   Expected Return = E(k) = ∑ kipi =

16.50%

Risk Return Trade-Off If you want higher return, we must be

prepared to take a bigger loss (higher risk)

If you want to reduce your risk of loss, you must sacrifice profit

Risk-Return Trade-off on Graph

0 0.5 1 1.5 2 2.505

101520253035

Return

Return

RISK

Measuring RiskSingle Asset

Standard Deviation: Square Root of Sum of Squared Deviations

Coefficient of Variation: Standard Deviation per Unit Return

Computing Standard Deviation

Economic Scenario Return(ki) (pi) kipi ki-E(k) [ki-E(k)]2 [ki-E(k)]2*pi Recession -5% .25 -1.25 21.5 462.25115.5625 Normal 18% .50 9.00 1.5 2.25

1.125 Boom 35% .25 8.75 18.5

342.25 85.5625 σ2 = 202.25 σ = 14.22

Risk Diversification Spreading Out Risk Ancient Sea-Farers’ Practice of

Distribution of Wares among Several Boats

Importance of Correlation Portfolio Risk of A Two-Asset Portfolio

Forming Two Asset Portfolio Weight Stock ExpectedStandard Return Deviation .40 A 18% 20% .60 B 22% 25% Correlation between Returns of A and B, ρAB = .6.   The expected return of this portfolio: E(kAB) = wAkA + wBkB = .40x18 + .60x22 = 20.4%. The general equation for expected return of a portfolio

of n assets : E(kA..N) = wAkA + wBkB + …. + Wnkn = ∑ wiki

Portfolio Risk Two Asset Portfolio St. Dev   σAB = √wA

2σA2+WB

2σB2+

2WAWBσAσBρAB

√.42*202 +.62*252 + 2*.4*.6*20*25*.4 = √.16*400 + .36 * 484 +

2*.24*500*.4 = 19.62

Preferred Portfolios and Efficient Portfolios

Preference for negative, 0, low correlations

Dominant Portfolios Efficient Frontier Efficient Portfolio

Reduction of Risk in Portfolio

ACI AMCL Apex Bd lmps Bata

0.110195 0.079549 0.312197 0.259559 0.104261 AMCL Apex BDlamps Bata

0.249513 0.191853 0.05602 0.208117 0.4154Correlation

Matrix

0.460216 0.430671 0.566614 0.870663 0.309745 ACI 0.584783 0.537449 0.495649 0.465433

-0.20165 -0.25761 -0.32954 -0.2231 -0.0614 AMCL 0.395016 0.392674 0.380887

0.072723 -0.022 0.224587 -0.14946 0.013006 Apex 0.404247 0.387296

1.629779 0.719224 1.276035 0.579072 1.011791 BDLamps 0.344365

1.875878 0.692234 0.814273 0.496051 0.512212

-0.11587 0.531855 0.340039 0.705045 0.688977 Standard Deviation of Portfolios

-0.13808 0.165363 0.535371 0.426668 0.274142 ACI-AMCL AAA AAAB AAABB Apex Bata

0.438079 0.281238 0.421733 0.352513 0.363126 Expected k .3597 .3804 .3734 .3713 .3924

0.775606 0.333596 0.457373 0.367931 0.34141 St Dev 0.503851 0.437989 0.421085 0.39193 .2983

Full Diversification

RISK

Diversifiable Risk Systematic Risk No. of

Assets

Systematic or market Risk Characteristic Line Beta

› Higher Beta (Greater Than 1): More Volatile than the Market. Characteristic Line Steep

› Low Beta (Less than 1): Less sensitive to market movements. Characteristic line flat

› Beta meaningful only in a portfolio context

› Draw a characteristic line› A quiz question

Capital Asset Pricing Model For accepting average risk, investor gets average premium over risk-free

rate, RP = (km-krf) Return, k

Market Return, km Market Risk Premium= (Km-Krf)Km

Risk- }Free Rate Krf

Risk Beta

1

Returns on DSE 20Year Dividend Yield Cap Gain Total Return %

2002 0.1096 -0.0194 9.44%

2003 0.0847 0.1643 36.11%

2004 0.0545 0.7576 81.24%

2005 0.0906 -0.2548 -16.51%

2006 0.0709 -0.1257 -5.42%

2007 0.0421 0.7676 80.98%

2008 0.0424 -0.0632 -2.08%

2009 0.0549 0.1223 18.14%

2010 0.0468 0.9916 104.48%Average Return

34.04%Standard Deviation

44.26%

Risk-Free Rate and Market Return in Bangladesh

Inflation = 7.5% Real (Lending) Interest Rate = 7-8.6% Real (Deposit) Interest Rate = 3.5%

(Suggested) Risk-Free Nominal Rate = About 11% Spread Between Deposit and Lending Rate:

About 5% Required Return for Long-term Debt = 15% Market Return = About 30 %

Impact of Inflation and Change in Risk Premium

Change in Inflation: Causes a parallel shift in the CML

Change in Risk-Premium: The slope of CML Changes.

Portfolio Beta and Portfolio Required Return

Portfolio Beta = Bp = Σ wibi

Portfolio Required Return = kp = krf + (km – krf) Betap

Stock Price Equilibrium What is required Return? What is expected Return? Which stock is overpriced?

Equilibrium Example Suppose you can buy a stock for Taka

250 today. You expect to sell it for Taka 310 one year from now. You will earn a dividend of Taka 50 over the year. What is your expected return?

Suppose the beta of the stock is 1.2. What is the required return?

Is the stock overpriced or underpriced?