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Two Asset Portfolio: Calculating Beta and Required Rate of Return

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Financial Concepts
Portfolio Theory, CAPM Homework
Homework Exercise 8

Rate of Return
Year Asset A Asset B Market
1 20.0% 19.0% 9.0%
2 -11.0% 22.0% 12.0%
3 10.0% -6.0% 6.0%
4 -9.0% -14.0% -4.0%
5 21.0% 28.0% 17.0%

For this exercise, you might want to copy and paste the table above into Excel and then do all your calculations on that spreadsheet.

1) Calculate the expected returns for Asset A, Asset B and the Market (use Average function in Excel)
Asset A =
Asset B =
Market =

2) Calculate the standard deviation of returns, ϭ, for each asset (use STDEVP function)
Asset A =
Asset B =
Market =

3) Calculate the correlation, ρ, between Asset A and Asset B (use CORREL function in Excel)

ρ =

4) Calculate the expected returns from the following portfolios:

Use the following formula to calculate the portfolio standard deviation
ϭP =√ (wAϭA)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))))^.5

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

Portfolio Expected Return Portfolio Std Dev.
% Asset A % Asset B
0% 100%
25% 75%
50% 50%
75% 25%
100% 0%

5) 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)

6) Calculate Beta for Asset A (relative to the Market) and Asset B relative to the Market) (use SLOPE function)

Beta for Asset A =
Beta for Asset B =

7) Assume that for next year the Risk Free Rate is expected to be 2% 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.

Required Return for Asset A =

Required Return for Asset B =

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Solution Summary

This solution determines the expected return on a two-asset portfolio. Using Excel, the expected returns and standard deviations for each asset and market are computed. Then, the efficient frontier is graphed using five possible portfolio options. Finally, the beta for each asset is calculated, and the expected return for each asset is computed using CAPM.

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1) Which security (A or B) has the least total risk? __________________
2) Which security (A or B) has the least systematic risk? __________________
3) Which security (A or B) has the greatest diversifiable risk? ____________________
4) What is the portfolio beta if you invest 35% in A, 45% in B and 20% in the risk-free asset?

Problem 2 (Chapter 13) Please use the following information to answer the following questions. The return on the risk-free asset is 4% and the return on the market is 14%.

Security Standard Deviation Beta
A 20% 1.2
B 25% 0.8

1) Which security (A or B) has the least total risk? __________________
2) Which security (A or B) has the least systematic risk? __________________
3) Which security (A or B) has the greatest diversifiable risk? ____________________
4) What is the portfolio beta if you invest 35% in A, 45% in B and 20% in the risk-free asset?
5) What is the portfolio expected return if you invest 35% in A, 45% in B and 20% in the risk-free asset?
6) What is the portfolio expected return if you invest 140% in A and the remainder in the risk-free asset via borrowing at the risk-free interest rate?
7) If you forecast the expected rates of returns for both Security A and security B, you get 14%. Which security should you buy/sell/hold as a result?

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