The market risk premium is 8 percent, and the risk-free rate is 4 percent. The s

ID: 2777356 • Letter: T

Question

The market risk premium is 8 percent, and the risk-free rate is 4 percent.

The standard deviation on Stock I's return is ______ percent, and the Stock I beta is_______ .

The standard deviation on Stock II's return is_____ percent, and the Stock II beta is____ .

Therefore, based on the stock's systematic risk/beta, is Stock I or Stock II "riskier"?

Assume these securities are correctly priced. Based on the CAPM, what is the expected return on the market?

What is the risk-free rate?

Consider the following information about Stocks I and II:

Explanation / Answer

Answer – Part I

Expected Return

Standard Deviation

Stock I

0.1355

0.33748

Stock II

0.084

0.302826

Based on the standard deviation, stock I appears to be “riskier” compared to stock II

Stock I

State of Economy

Probability

Rate of Return

Recession

0.25

0.05

Normal

0.45

0.20

Irrational Exuberance

0.30

0.11

Expected return = 0.25 * 0.05 + 0.45 * 0.20 + 0.30 * 0.11

= 0.0125 + 0.09 + 0.033

= 0.1355

Variance = 0.25 * (0.05-0.1355)^2 + 0.45*(0.20-0.1355)^2+0.30*(0.11-0.1355)^2

= 0.25 * (-0.0855)^2 + 0.45 * 0.0645^2 + 0.30 * (-0.0255)^2

= 0.0018275625 + 0.0018721125 + 0.000195075

= 0.11389475

Standard Deviation = Square root (Variance) = (0.11389475)^1/2 = 0.33748

Stock II

State of Economy

Probability

Rate of Return

Recession

0.25

-0.36

Normal

0.45

0.08

Irrational Exuberance

0.30

0.46

Expected Return = 0.25 * -0.36 + 0.45 * 0.08 + 0.3 * 0.46

= -0.09 + 0.036 + 0.138

= 0.084

Variance = 0.25*(-0.36-0.084)^2 + 0.45 * (0.08-0.084)^2 + 0.3 * (0.46-0.084) ^2

= 0.25 * (-0.444)^2 + 0.45 * (-0.004)^2 + 0.3 * (0.376)^2

= 0.049284 + 0.0000072 + 0.0424128

= 0.091704

Standard Deviation = Square root(Variance) = (0.091704)^1/2 = 0.302826

Answer Part II

Expected Return on Market = 11.32%

Risk-free rate = 2.62%

Let rm and rf represent market return and risk-free rate respectively. Then as per CAPM

Expected return = rf + Beta * (rm-rf)

For Pete Corp

0.135 = rf + 1.25* (rm-rf) ----(1)

For Repete Co

0.108 = rf + 0.94 *(rm-rf) ---(2)

Subtracting Equation (2) from (1) and re-arranging the terms

0.135 – 0.108 = rf + 1.25* (rm-rf) – rf - 0.94 *(rm-rf)

0.027 = 1.25 rm – 0.94 rm – 1.25 rf + 0.94 rf

0.027 = 0.31 rm – 0.31 rf

(rm-rf) * 0.31 = 0.027

rm-rf = 0.027 / 0.31 = 0.087097

Substituing value of rm-rf in equation (1)

0.135 = rf + 1.25* 0.087097

rf = 0.135 - 1.25* 0.087097 = 0.135 – 0.10887 = 0.026129 or 2.6129% or 2.62% (rounded off)

Substituting value of rf in equation (2)

0.108 = 0.026129 + 0.94 *(rm-0.026129)

0.108 = 0.026129 + 0.94 rm – 0.02456126

0.94* rm = 0.108 – 0.026129 + 0.02456126

0.94* rm = 0.10643226

rm = 0.10643226 /0.94 = 0.113225 or 11.32%