### How much of each bond will you hold in your portfolio

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Q.1 A 9-year bond has a yield of 10% and a duration of 7.194 years. If the market yield changes by 50 basis points, what is the percentage change in the bond's price?

Q.2. Find the duration of a 6% coupon bond making annual coupon payments if it has maturity and has a yield to maturity of 6%. What is the duration if the yield to maturity is 10%. Find the duration of the bond if the coupons are paid semiannually.

Q.3 You are managing a portfolio of \$1 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity of 5 years, and a perpetuity, each currently yielding 5%.

a. How much of each bond will you hold in your portfolio?

b. How will these fractions change next year if target duration is now 9 years?

Q.4 Bonds of Zello Corporation with a par value of \$1,000 sell for \$960, mature in 5 years, and have a 7% annual coupon rate paid semiannually.

a. Calculate each of the following yields:
i. Current yield.
ii. Yield to maturity (to the nearest whole percent, i.e., 3%, 4%. 5%, etc.).
iii. Horizon yield (also called total compound return) for an investor with a 3-year period and a reinvestment rate of 6% over the period. At the end of 3 years the 7% coupon bonds with 2 years remaining will sell to yield 7%.

b. Cite a major shortcoming for each of the following fixed-income yield measures:
i. Current yield.
ii. Yield to maturity.
iii. Horizon yield (also called total compound return).

Q.5 Carol Harrod is the investment officer for a \$100 million U.S. pension fund. The fixed - income portion of the portfolio is actively managed, and a substantial portion of the fund's large capitalization U.S. equity portfolio is indexed and managed by Webb Street Advisors.

Harrod has been impressed with the investment results of Webb Street's equity index strat¬egy and is considering asking Webb Street to index a portion of the actively managed fixed-income portfolio.

a. Describe advantages and disadvantages of bond indexing relative to active bond management.

b. Webb Street manages indexed bond portfolios. Discuss how an indexed bond portfolio is constructed under stratified sampling (cellular) methods.

c. Describe the main source of tracking error for the cellular method.

Q.6A manager buys three shares of stock today, and then sells one of those shares each year for: next 3 years. His actions and the price history of the stock are summarized below. The stockpra no dividends.

 Time Price Action 0 \$90 Buy 3 shares 1 100 Sell 1 share 2 100 Sell 1 share 3 100 Sell 1 share

a. Calculate the time-weighted geometric average return on this "portfolio."

b. Calculate the time-weighted arithmetic average return on this portfolio.

c. Calculate the dollar-weighted average return on this portfolio.

Q 7. Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 6%, and the market's average return was 14%. Performance is measured using an index model regression on excess returns.

Stock A                  Stock B

Index model regression estimates                   1% + 1.2(rm- rf)        2% + .8(rm - rf)

R-square                                                      .576                              .436

Residual standard deviation, 0(e)                      10.3%                            19.1%

Standard deviation of excess returns                 21.6%                            24 9%

a. Calculate the following statistics for each stock:

i. Alpha
ii. Information ratio
iii. Sharpe ratio
iv. Treynor measure

b. Which stock is the best choice under the following circumstances?
i. This is the only risky asset to be held by the investor.
ii. This stock will be mixed with the rest of the investor's portfolio, currently composed solely of holdings in the market-index fund.
iii. This is one of many stocks that the investor is analyzing to form an actively managed stock portfolio.

Q 8. Consider the following information regarding the performance of a money manager in a recent month. The table represents 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 1 and the returns of sector indices in column 4.

 Actual Return Actual Weight Benchmark Weight Index Return Equity 2% .70 .60 2.5% (S&P 500) Bonds 1 .20 .30 1.2 (Salomon Index) Cash 0.5 .10 .10 0.5

a. What was the manager's return in the month? What was her overperformance or underperformance?
b. What was the contribution of security selection to relative performance?
c. What was the contribution of asset allocation to relative performance? Confirm that the sum of selection and allocation contributions equals her total "excess" return relative to the bogey.

Q 9. A global equity manager is assigned to select stocks from a universe of large stocks through, out the world. The manager will be evaluated by comparing her returns to the return on the MSC! World Market Portfolio, but she is free to hold stocks from various countries in whatever proportions she finds desirable. Results for a given month are contained in the following table

 Country Weight In MSCI Index Manager's Weight Managers Return in Country Return of Stock Index for That Country U.K. .15 .30 20% 12% Japan .30 .10 15 15 U.S. .45 .40 10 14 Germany .10 .20 5 12

a. Calculate the total value added of all the manager's decisions this period.
b. Calculate the value added (or subtracted) by her country allocation decisions.
c. Calculate the value added from her stock selection ability within countries. Confirm th sum of the contributions to value added from her country allocation plus security self decisions equals total over- or underperformance.

Q 10. Kelli Blakely is a portfolio manager for the Miranda Fund (Miranda), a core large-cap equity fund. The market proxy and benchmark for performance measurement purposes is the S&P 500. Although the Miranda portfolio generally mirrors the asset class and sector weightings of the S&P. Blakely is allowed a significant amount of leeway in managing the fund. Her portfolio holds only stocks found in the S&P 500 and cash.

Blakely was able to produce exceptional returns last year (as outlined in the table below) through her market timing and security selection skills. At the outset of the year, she became extremely concerned that the combination of a weak economy and geopolitical uncertainties would negatively impact the market. Taking a bold step. she changed her market allocation. For the entire year her asset class exposures averaged 50% in stocks and 50% in cash. The S&P's allocation between stocks and cash during the period was a constant 97% and 3%, respectively. The risk-free rate of return was 2%.

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