## Transcribed Text

Investment Analysis & Portfolio Management
The table contains the annual rates of return for 2 specific assets
and also the market as a whole (like the S&P 500 Index)
Year Asset A Asset B Market
1 -11% 18% 15%
2 9% 12% -6%
3 20% -5% 12%
4 -7% -13% -11%
5 17% 24% 16%
1)
Expected
Returns Asset A Asset B Market
2)
Std. Dev. of
Returns Asset A Asset B Market
3) Calculate the Coefficient of Variation (CV) for each of the three
Asset A Asset B Market
4)
Asset A &
B
Asset A
&
Market
Asset B &
Market
5) Calculate the expected returns from the following portfolios:
Use the following formula to calculate the portfolio standard deviation
Rate of Return
Calculate the expected returns for Asset A, Asset B and the Market
(hint: use Average function in Excel)
Calculate the standard deviation of returns, ϭ, for each asset
(hint:use STDEVP function)
Coefficient of
Variation
Calculate the correlation of returns , ρ, between Asset A and Asset
B; Asset A and the Market as a whole; and Asset B and the Market
as a whole (hint: use CORREL function)
Correlation of
Returns
ϭP
=√ ((wAσA)
2
+(wBϭB)
2
+(2 wA wB ϭA ϭB ρ(A,B))
=(((wA*ϭA)^2) +((wB *ϭB )^2)+(2 *wA* wB *ϭA *ϭB *ρ(A,B))^0.5
% Asset A % Asset B
0% 100%
20% 80%
40% 60%
60% 40%
80% 20%
100% 0%
6)
7)
Beta
Asset A &
Market
Asset B
&
Market
Where wA and wB are the % of assets in Asset A and B respectively
ϭA and ϭB are the respective standard deviations of return and
ρ(A,B)).is the correlation of returns between asset A and B
Using Portfolio Expected Returns on the Y axis and Portfolio Standard
Deviation in the X axis, draw the efficient frontier for possible portfolio
combinations of Asset A and B. (include 100% A and 100% B as two
possibilities). (Hint: Use the Excel Chart Wizard and select the XY(scatter)
plot option)
Calculate Beta for Asset A relative to the Market and Asset B relative to the
Market (Hint: use SLOPE function or βi
= (Ϭi
x ρi,M) / ϬM )
Portfolio Mix Portfolio
Expected
Return
Portfolio
Std Dev.
0%
20%
40%
60%
80%
100%
120%
0% 20% 40% 60% 80% 100% 120%
Expected Portfolio Return
Portfolio Risk (Std. Dev)
Portfolio Risk vs. Return
8)
2%
12%
Required
Return Asset A Asset B
9)
Investment Beta
Proportion
of
Portfolio
Beta x
Proportion
Mutual Fund A 0.9 0.0%
Mutual Fund B 1.4 0.0%
Total $120,000
Weighted
Average =
10)
3%
6%
Beta
Required
Return
0.8
1.2
11)
Stock Investment Beta
A $400,000 1.5
B 600,000 -0.5
C 1,000,000 1.25
D 2,000,000 0.75
Total Portfolio $4,000,000
Assume that for next year the Risk Free Rate is expected to be 3% and that the
overall market will realize a return of 12%. Using the CAPM / SML
methodology, calculate the required returns for Asset A and Asset B.
Risk Free Rate =
Expected Market Return =
An individual has portfolio totalling $120,000. 60% in invested in a mutual
fund with a beta of 0.9 and 40% invested in another mutual fund with a beta
of 1.4. If these are the only two investments in her portfolio, what is the
Assume that the risk free rate is 3% and that the market risk premium is 6%.
What is the required return on a stock with a beta of 1.0 and on a stock with a
beta of 0.8?
Risk Free Rate =
Market Risk Premium =
Suppose you manage the $4 million portfolio that consists of four
stocks with the following investments:
6%
14%
Stock Investment Beta Required
Return
Portfolio
Share
A $400,000 1.5
B 600,000 -0.5
C 1,000,000 1.25
D 2,000,000 0.75
Total Portfolio $4,000,000
Weighted
Average =
12)
Number
of
Securitie
s Value Beta
20 2,000,000 1.1
1 100,000 0.9
1 100,000 1.4
13)
Expected Market Return =
If the market’s expected rate of return is 14% and the risk-free rate
is 6%, what is the portfolio’s required rate return?
Risk Free Rate =
You are a consultant to a large manufacturing company tht is considering a
project with the followiing net after tax cash flows:
New Portfolio
Prior Porfolio
Security Sold
Residual Porfolio
New Security Purchased
You have a $2 million portfolio consisting of $100,000 investment in each of
20 different stocks. The portfolio has a beta of 1.1. You are considering
selling $100,000 worth of one stock with a beta of 0.9 and using the proceeds
to purchase another stock with a beta of 1.4 what will be the portfolio’s new
beta after these transactions?
Year Cash flow
0 (net investment) -40
1 through 10 11
N = 10
rRF = 3%
rM = 14%
β= 1.60
a) What is the Net Present Value (NPV) for the project?
b) What is the highest possible Beta estimate for the project before its NPV
would become negative?
The project's Beta is 1.6. Assuming that the risk free rate (rRF) is 3% and the
expected market return (rM) from other available investments is 14%:

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