Question

Consider the following statistics of the returns of Stock A, Stock B and the market (m):

s_{A} =
0.20 corr_{A,m} = 0.4

s_{B} =
0.30 corr_{B,m} = 0.7

s_{m} = 0.15

E(r_{m}) = 0.10

Suppose further that the risk-free rate is 5%.

(a) According to the Capital Asset Pricing Model, what should be the expected return of Stock A and of Stock B? [Hint: This is an open-book exam.]

(b) Suppose that the correlation between the return of Stock A and the return of Stock B is 0.5. What are the expected return and the standard deviation of the return of a portfolio that has a 40% investment in Stock A and a 60% investment in Stock B?

(c) Assume that the Capital Asset Pricing Model is valid. How could you construct a new portfolio (P) using the market portfolio (m) and the risk-free asset that has the same expected return as the portfolio you considered in part (b)? What is the standard deviation of the return of this portfolio (P)?

(d) i) Suppose that the correlation between the return of Stock A and the return of Stock B is -0.7. What are the expected return and the standard deviation of the return of a portfolio that has a 40% investment in Stock A and a 60% investment in Stock B? Explain the difference in value between the standard deviations of the return of the portfolios in parts (c) and (d).

ii) Consider an investment that is made up of a combination of the risky portfolio in (i) and the risk-free asset. In this case, would it be advisable to switch to a portfolio made up of the market portfolio and the risk-free asset? In other words, is the market portfolio mean-variance efficient in this case? [Hint: Consider the measure that captures the risk- return trade-off.]

Answer #1

Covariance(Asset1,2) =Correlation (Asset1,2)*Standard Deviation Asset1*Standard Deviation Asset2 | ||||||||

Covariance A,m=corrA,m*SA*Sm | ||||||||

Covariance A,m=0.4*0.2*0.15= | 0.012 | |||||||

Covariance B,m=corrB,m*SB*Sm | ||||||||

Covariance B,m=0.7*0.3*0.15= | 0.0315 | |||||||

Beta of Stock A=Covariance A,m/Variance of market Return | ||||||||

Variance of market return =sm^2=0.15^2= | 0.0225 | |||||||

Beta of Stock A=Ba=0.012/0.0225 | 0.533333 | |||||||

Beta of Stock B=Covariance B,m/Variance of market Return | ||||||||

Variance of market return =sm^2=0.15^2= | 0.0225 | |||||||

Beta of Stock B=Bb=0.0315/0.0225 | 1.4 | |||||||

(a) | CAPM equation: | |||||||

Rs=Rf+Beta*(Rm-Rf) | ||||||||

Rs=Expected Return of Stock | ||||||||

Rm=Expected market return= | 0.1 | |||||||

Rf=Risk Free rate=5% | 0.05 | |||||||

Ra=Expected Return of A=0.05+Ba*(0.1-0.05) | ||||||||

Ra=Expected Return of A=0.05+0.53333*(0.1-0.05) | 0.0767 | |||||||

Rb=Expected Return of B=0.05+Bb*(0.1-0.05) | ||||||||

RB=Expected Return of B=0.05+1.4*(0.1-0.05) | 0.1200 | |||||||

(b) | CovarianceA, B,=corrA,B,*SA*SB | |||||||

Covariance A,B=0.5*0.2*0.3= | 0.03 | |||||||

Portfolio Return=Rp=wa*Ra+wb*Rb | ||||||||

wa=Weight of A in the portfolio | 0.4 | |||||||

wb=Weight of B in the portfolio | 0.6 | |||||||

Rp=Portfolio Return =0.4*0.0767+0.6*0.12 | 0.1027 | |||||||

Portfolio Variance =Vp= (wa^2)*(SA^2)+(wb^2)*(SB^2)+2*wa*wb*Covariance A,B | ||||||||

Portfolio Variance =Vp= (0.4^2)*(0.2^2)+(0.6^2)*(0.3^2)+2*0.4*0.6*0.03 | ||||||||

Vp=Portfolio Variance | 0.0532 | |||||||

Sandard Deviation of the portfolio=Sqiuare Root (Variance) | 0.2307 | (SQRT(0.0532) | ||||||

.(c) | wm=Weight of market portfolio | |||||||

wf=Weight of Risk Free Asset=1-wm | ||||||||

Portfolio Return =0.1027=wm*0.1+wf*0.05 | ||||||||

wm*0.1+(1-wm)*0.05=0.1027 | ||||||||

0.05wm=0.1027-0.05= | 0.0527 | |||||||

wm=0.0527/0.05= | 1.053333 | |||||||

wf=1-1.05333= | -0.05333 | |||||||

This means Take Loan at risk free rate and invest in market | ||||||||

Standard Deviation of Risk Free rate (Sf)=0 | ||||||||

Covariance f,m=0 | ||||||||

Vp=Portfolio Variance =(wm^2)*(Sm^2) | ||||||||

Portfolio Standard Deviation=Square Root of Vp=wm*Sm | 0.158 | (1.05333*0.15) | ||||||

(d) | Covariance A,B=-0.7*0.2*0.3= | -0.042 | ||||||

wa=Weight of A in the portfolio | 0.4 | |||||||

wb=Weight of B in the portfolio | 0.6 | |||||||

Rp=Portfolio Return =0.4*0.0767+0.6*0.12 | 0.1027 | |||||||

Portfolio Variance =Vp= (wa^2)*(SA^2)+(wb^2)*(SB^2)+2*wa*wb*Covariance A,B | ||||||||

Portfolio Variance =Vp= (0.4^2)*(0.2^2)+(0.6^2)*(0.3^2)+2*0.4*0.6*(-0.042) | ||||||||

Vp=Portfolio Variance | 0.01864 | |||||||

Sandard Deviation of the portfolio=Sqiuare Root (Variance) | 0.1365 | (SQRT(0.01864) | ||||||

Expected Portfolio Return =Rp=wa*Ra+wb*Rb | 0.1027 | |||||||

Return remains the same, but Standard deviation is decreased significantly | ||||||||

ii) | Reward/Risk Ratio of the portfolio =Rp/Standard Deviation | 0.75198 | (0.1027/0.1365) | |||||

Reward/Risk Ratio of the Market =Rm/Sm | 0.666667 | (0.1/0.15 | ||||||

Reward /Risk ratio of the portfolio is higher | ||||||||

It will not be advisable to switch to market+riskfree asset | ||||||||

The standard deviation of Asset A returns is 36%, while the
standard deviation of Asset M returns is 24%. The correlation
between Asset A and Asset M returns is 0.4.
(a) The average of Asset A and Asset M’s standard deviations is
(36+24)/2 = 30%. Consider a portfolio, P, with 50% of funds in
Asset A and 50% of funds in Asset M. Will the standard deviation of
portfolio P’s returns be greater than, equal to, or less than 30%?...

Consider the following capital market: a risk-free asset
yielding 2.25% per year and a mutual fund consisting of 80% stocks
and 20% bonds. The expected return on stocks is 13.25% per year and
the expected return on bonds is 3.95% per year. The standard
deviation of stock returns is 40.00% and the standard deviation of
bond returns 14.00%. The stock, bond and risk-free returns are all
uncorrelated.
a. What is the expected return on the mutual
fund? 11.39
b. What is...

Consider the following capital market: a risk-free asset
yielding 2.75% per year and a mutual fund consisting of 65% stocks
and 35% bonds. The expected return on stocks is 13.25% per year and
the expected return on bonds is 4.75% per year. The standard
deviation of stock returns is 42.00% and the standard deviation of
bond returns 14.00%. The stock, bond and risk-free returns are all
uncorrelated.
What is the expected return on the mutual fund?
What is the standard...

Suppose that many stocks are traded in the market and that it is
possible to borrow at the risk-free rate, rƒ. The characteristics
of two of the stocks are as follows: Stock Expected Return Standard
Deviation A 5 % 45 % B 10 % 55 % Correlation = –1 a. Calculate the
expected rate of return on this risk-free portfolio? (Hint: Can a
particular stock portfolio be substituted for the risk-free asset?)
(Round your answer to 2 decimal places.)

A portfolio that combines the risk-free asset and the market
portfolio has an expected return of 7.4 percent and a standard
deviation of 10.4 percent. The risk-free rate is 4.4 percent, and
the expected return on the market portfolio is 12.4 percent. Assume
the capital asset pricing model holds.
What expected rate of return would a security earn if it had a .49
correlation with the market portfolio and a standard deviation of
55.4 percent? Enter your answer as a percent...

Suppose that many stocks are traded in the market and that it is
possible to borrow at the risk-free rate, rƒ. The characteristics
of two of the stocks are as follows: Stock Expected Return Standard
Deviation A 6 % 20 % B 10 % 80 % Correlation = –1 a. Calculate the
expected rate of return on this risk-free portfolio? (Hint: Can a
particular stock portfolio be substituted for the risk-free asset?)
(Round your answer to 2 decimal places.) Rate...

Suppose that many stocks are traded in the market and that it is
possible to borrow at the risk-free rate, rƒ.
The characteristics of two of the stocks are as follows:
Stock
Expected Return
Standard Deviation
A
12
%
40
%
B
21
%
60
%
Correlation = –1
a. Calculate the expected rate of return on this
risk-free portfolio? (Hint: Can a particular stock
portfolio be substituted for the risk-free asset?) (Round
your answer to 2 decimal places.)
b....

Assume for parts (a) to (c) that the Capital Asset Pricing Model
holds. The market portfolio has an expected return of 5%. Stock A's
return has a market beta of 1.5, an expected value of 7% and a
standard deviation of 10%. Stock B's return has a market beta of
0.5 and a standard deviation of 20%. The correlation between stock
A's and stock B's returns is 0.5.
1.what the risk-free rate? What is the expected return on stock
B?...

Suppose that many stocks are traded in the market and that it is
possible to borrow at the risk-free rate, rf .
The characteristics of two of the stocks are as follows:
Stock
Expected Return
Standard Deviation
A
10
%
35
%
B
16
65
Correlation = –1
Required:
(a)
Calculate the expected rate of return on this risk-free
portfolio. (Hint: Can a particular stock portfolio be
substituted for the risk-free asset?) (Omit the "%" sign in
your response. Round...

ABC allows employees to purchase two stocks (Stock A and Stock
B) to sustain their retirement portfolio. Suppose that there are
many stocks in the market, and that the characteristics of Stocks A
and B are given as follows:
Stock Expected return Standard deviation
A 10% 5%
B 15% 10%
Note: Correlation = -1
Suppose it is possible to borrow at the risk-free rate, Rf. What
must be the value of the risk-free rate?(Hint: think about
constructing a...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 12 minutes ago

asked 27 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago