. Calculate and compare the alpha of the two managers relative to each other and to the S&P 500.

7. Consider the following information regarding the performance of a money manager in a
recent month. The table presents the actual return of each sector of the manager’s portfolio
in column (1), the fraction of the portfolio allocated to each sector in column (2), the
benchmark or neutral sector allocations in column (3), and the returns of sector indexes in
column (4).
2. 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 portfolios consist primarily of common stocks, cash reserves are included in the calculation
of both portfolio betas and performance. By way of perspective, selected data for
the financial markets are included in the following table. (LO 18-1)
Total Return Beta
Manager A 24.0% 1.0
Manager B 30.0 1.5
S&P 500 21.0
Lehman Bond Index 31.0
91-day Treasury bills 12.0
a. Calculate and compare the alpha of the two managers relative to each other and to the
S&P 500.
b. Explain two reasons the conclusions drawn from this calculation may be misleading.
3. 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.
Th e plan’s board of trustees directed Karl fi ve years 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. Th ey also noted a state statute 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
Asset Mix as of 9/30/20
At Cost
(millions)
At Market
(millions)
Fixed-income assets:
Short-term securities $ 4.5 11.0% $ 4.5 11.4%
Long-term bonds and mortgages 26.5 64.7 23.5 59.5
Common stocks 10.0 24.3 11.5 29.1
$41.0 100.0% $39.5 100.0%
INVESTMENT PERFORMANCE
Annual Rates of
Return for Periods
Ending 9/30/20
5 Years 1 Year
Total Alpine Fund:
Time-weighted 8.2% 5.2%
Dollar-weighted (Internal) 7.7% 4.8%
Assumed actuarial return 6.0% 6.0%
U.S. Treasury bills 7.5% 11.3%
Large sample of pension funds
(average 60% equities, 40% fixed income) 10.1% 14.3%
Common stocks—Alpine Fund 13.3% 14.3%
Average portfolio beta coefficient 0.90 0.89
Standard & Poor’s 500 Stock Index 13.8% 21.1%
Fixed-income securities—Alpine Fund 6.7% 1.0%
Salomon Brothers’ Bond Index 4.0% 211.4%
Karl was proud of his performance and was chagrined when a trustee made the following
critical observations:
a. “Our one-year results were terrible, and it’s what you’ve done for us lately that
counts most.”
b. “Our total fund performance was clearly inferior compared to the large sample of other
pension funds for the last five years. What else could this reflect except poor management
judgment?”
c. “Our common stock performance was especially poor for the five-year period.”
d. “Why bother to compare your returns to the return from Treasury bills and the actuarial
assumption rate? What your competition could have earned for us or how we would
have fared if invested in a passive index (which doesn’t charge a fee) are the only relevant
measures of performance.”
e. “Who cares about time-weighted return? If it can’t pay pensions, what good is it!”
Appraise the merits of each of these statements and give counterarguments that Karl
can use. (LO 18-2)
4. A portfolio manager summarizes the input from the macro and micro forecasts in the following
table: MICRO FORECASTS
Asset Expected Return (%) Beta
Residual Standard
Deviation (%)
Stock A 20 1.3 58
Stock B 18 1.8 71
Stock C 17 0.7 60
Stock D 12 1.0 55
MACRO FORECASTS
Asset Expected Return (%) Standard Deviation (%)
T-bills 8 0
Passive equity portfolio 16 23
a. Calculate expected excess returns, alpha values, and residual variances for these stocks.
b. Construct the optimal risky portfolio.
c. What is Sharpe’s measure for the optimal portfolio and how much of it is contributed
by the active portfolio? What is the M 2 ?