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Essentials of Investments (BKM 5th

Ed.)

Answers to Selected Problems Lecture 6

Chapter 5:

14b. Time Cash flow Explanation

0 300 Purchase of three shares at $100 each.1 208 Purchase of two shares at $110 less dividend income on three shares held.2 110 Dividends on five shares plus sale of one share at price of $90 each.3 396 Dividends on four shares plus sale of four shares at price of $95 each.

396|||

110 |

| |Date: 1/1/96 1/1/97 1/1/98 1/1/99

| || || || 208

300

The Dollar-weighted return can be determined by doing an internal rate of return (IRR)calculation. In other words, set the present value of the outflows equal to the presentvalue of the inflows (or the net present value to zero):

%1661.0001661.0)1(

396

)1(

110

)1(

208300

321==

+

+

+

=

+

+

RRR

Chapter 20:

3. b.

5. We need to distinguish between timing and selection abilities. The intercept of the scatterdiagram is a measure of stock selection ability. If the manager tends to have a positive

excess return even when the markets performance is merely neutral (i.e., has zero excessreturn), then we conclude that the manager has on average made good stock picks stockselection must be the source of the positive excess returns.

Timing ability is indicated by curvature in the plotted line. Lines that become steeper asyou move to the right of the graph show good timing ability. An upward curvedrelationship indicates that the portfolio was more sensitive to market moves when themarket was doing well and less sensitive to market moves when the market was doing

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poorly -- this indicates good market timing skill. A downward curvature would indicatepoor market timing skill.

We can therefore classify performance ability for the four managers as follows:

Selection Ability Timing Abilitya. Bad Goodb. Good Goodc. Good Badd. Bad Bad

9. The managers alpha is:

10 - [6 + 0.5(14-6)] = 0

10. a) (A) = 24 - [12 + 1.0(21-12)] = 3.0%(B) = 30 - [12 + 1.5(21-12)] = 4.5%T(A) = (24 - 12)/1 = 12T(B) = (30-12)/1.5 = 12

As an addition to a passive diversified portfolio, both A and B are candidates becausethey both have positive alphas.

b) (i) The funds may have been trying to time the market. In that case, the SCL of thefunds may be non-linear (curved).

(ii) One years worth of data is too small a sample to make clear conclusions.

(iii) The funds may have significantly different levels of diversification. If both havethe same risk-adjusted return, the fund with the less diversified portfolio has ahigher exposure to risk because of its higher firm-specific risk. Since the abovemeasure adjusts only for systematic risk, it does not tell the entire story.

11. a) Indeed, the one year results were terrible, but one year is a short time period from whichto make clear conclusions. Also, the Board instructed the manager to give priority to long-term results.

b) The sample pension funds had a much larger share in equities compared to Alpines.Equities performed much better than bonds. Also, Alpine was told to hold down riskinvesting at most 25% in equities. Alpine should not be held responsible for an assetallocation policy dictated by the client.

c) Alpines alpha measures its risk-adjusted performance compared to the markets:

= 13.3 - [7.5 + 0.9(13.8 - 7.5)] = 0.13%, which is actually above zero!

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d) Note that the last five years, especially the last one, have been bad for bonds andAlpine was encouraged to hold bonds. Within this asset class, Alpine did much better thanthe index funds. Alpines performance within each asset class has been superior on a risk-adjusted basis. Its disappointing performance overall was due to a heavy asset allocation

weighting toward bonds, which was the Boards not Alpines choice.

e) A trustee may not care about the time-weighted return, but that return is moreindicative of the managers performance. After all, the manager has no control over thecash inflow of the fund.