Problem 1: During a particular year, the T-bill rate was 6%, the market return was 14%, and a portfolio manager with beta of .5 realized a return of 10%. Evaluate the manager based on the portfolio alpha.
Problem 2: Go to www.mhhe.com/bkm, where you will find five year of monthly returns for two mutual funds, Vanguard U.S. Growth Fund and U.S. Value Fund, as well as corresponding returns for the S&P 500 and the Treasury bill rate.
A. Set up a spreadsheet to calculate each fund's excess rate of return over T-bills in each month.
B. Calculate the standard deviation of each fund over the five-year period.
C. What was the beta of each fund over the five year period?
D. What were the Sharpe, Jensen, and Treynor measures for each fund?
CFA Problems:
1. A plan sponsor with a portfolio manager who invest in small capitalization, high growth stocks should have the plan sponsor's performance measured against which one of the following?
a. S&P Index.
b. Wilshire 5000 Index.
c. Dow Jones Industrial Average.
d. Russell 2000 Index.
2. Assume you purchased a rental property for $50,000 and sold it one year later for $55,000 (there was no mortgage on the property). At the time of the sale, you paid $2,000 in commissions and $600 in taxes. If you received $6,000 in rental did you earn? (All of it received at the end of the year), what annual rate of return did you earn?
3. A two year investment of $ 2,000 results in a return of $150 at the end of the first year and a return of $ 150 at the end of the second year, in addition to the return of the original investment. What is the internal rate of return on the investment?
4. The chairman provides you with the following data, covering one year, concerning the portfolios of two of the fund's equity managers (manager A and manager B). Although the portfolio consists primarily of common stocks, cash reserves are included in the calculation of both portfolios betas and performance. By way of perspective, selected data for the financial markets are includes in the following table.
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Total Return
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Beta
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Manager A
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24.0%
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1.0
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Manager B
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30.0
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1.5
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S&P 500
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21.0
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|
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Lehman Bond Index
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31.0
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|
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91-day Treasury bills
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12.0
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a. Calculate and compare the risk adjusted performance of the two managers relative to each other and to the S&P 500.
b. Explain two reasons the conclusions may be misleading.
5. Carl Karl, a portfolio manager for the Alpine Trust Company, has been responsible since 2015 for the City of Alpine's Employee Retirement Plan, a municipal pension fund.
Alpine is a growing community, and city services and employee payrolls have expanded in each of the past 10 years. Contributions to the plan in fiscal 2020 exceeded benefit payments by a three to one ratio.
The plan's Board of Trustees directed Karl five year ago to invest for total return over the long term. However, as trustees of this highly visible public fund, they cautioned him that volatile or erratic results could cause them embarrassment, they also noted a state statue that mandated that not more than 25% of the plan's assets (at cost) be invested in common stocks.
At the annual meeting of the trustees in November 2020, Karl presented the following portfolio and performance report to the board.
ALPINE EMPLOYEE RETIREMENT PLAN
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Assets Mix as of 9/30/20
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At Cost (millions)
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At the Market (millions)
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Fixed Income assets:
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$ 4.5 11.0%
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$ 4.5 11.4%
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Short term securities
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26.5 64.7%
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23.5 59.5
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Long term bonds and mortgages
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10.0 24.3
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11.5 29.1
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Common stocks
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$41.0 100.0%
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$39.5 100.0%
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