Investments & Securities Chapter 24 Which stock has greater dispersion around the mean

Inputs:

Date Amount

1/1/2010 -148000

1/3/2010 2500

3/20/2010 4000

7/5/2010 1500

12/2/2010 13460

3/10/2011 -23000

4/7/2011 3000

5/3/2011 198000

0.265007

Problem 24-01

A household (HH) savings-account spreadsheet shows the following entries:

Date Additions Withdrawals Value

1/1/10 148,000

1/3/10 2,500

3/20/10 4,000

7/5/10 1,500

12/2/10 13,460

3/10/11 23,000

4/7/11 3,000

5/3/11 198,000

Inputs:

Year rABC rXYZ rABC rXYZ

Geo data Geo data

1 0.20 0.32 1.2 1.32

2 0.12 0.12 1.12 1.12

3 0.19 0.19 1.19 1.19

4 0.04 0.01 1.04 1.01

5 0.02 -0.07 1.02 0.93

return

w/equal

probabilit

y

0.1140

d.2.

Expected

rate of

return

w/unequa

l

Answers:

Problem 24-05

Consider the rate of return of stocks ABC and XYZ.

Year rABC rXYZ

1 20% 30%

2 12 12

3 14 18

4 3 0

Geometric Average

rABC %

rXYZ %

d-1.If you were equally likely to earn a return of 20%, 12%, 14%, 3%, or 1%, in each year (these are the five annual returns

for stock ABC), what would be your expected rate of return? (Do not round intermediate calculations. Omit the “%” sign

in your response.)

Expected rate of return %

b.

Dispersion

Inputs:

Shares

bought/so

2016 160 2 4 2016 640 8648

-2.0581%

Yr Return

2013-2014 0.0750

2014-2015 -0.1647

2015-2016 0.1571

Arithmetic

average

0.0225

rate of

Answers:

a.

weighted

Arithmeti

c average

Problem 24-06

XYZ stock price and dividend history are as follows:

Year Beginning-of-Year Price Dividend Paid at Year-End

An investor buys three shares of XYZ at the beginning of 2013, buys another two shares at the beginning of

2014, sells one share at the beginning of 2015, and sells all four remaining shares at the beginning of 2016.

a.What are the arithmetic and geometric average time-weighted rates of return for the investor?

(Round your

year-by-year rates of return and final answer to 2 decimal places. Do not round other calculations. Round

your answers to 2 decimal places. Omit the “%” sign in your response.)

Arithmetic average rate of return %

2013 160 2-3 2013 -480 -480

2014 170 2-2 2014 -340 6 -334

2015 140 2 1 2015 140 10 150

Inputs:

Time Price Action CF HPR

080 Buy 3 shares -240

190 Sell 1 share 90 0.125

290 Sell 1 share 90 0

390 Sell 1 share 90 0

Answers:

a.

Geometri

c average

return %

4.00%

Problem 24-07

A manager buys three shares of stock today, and then sells one of those shares each year for the next 3 years. His

actions and the price history of the stock are summarized below. The stock pays no dividends.

Time Price Action

0 $90 Buy 3 shares

Arithmetic average return %

c.Calculate the dollar-weighted average return on this portfolio. (Do not round intermediate calculations. Round

your answer to 2 decimal places. Omit the “%” sign in your response.)

Dollar-weighted average return %

Inputs:

Stock Alpha Beta rM rf

Index

model

regression

Residual

standard

deviation,

σ(e)

0.118 0.206

of excess

Standard

deviation

Answers:

Stock A Stock B

a.

i. Alpha 0.01 0.02

ii.

Informati

on ratio

Sharpe

0.0847 0.0971

iv.

6.8333% 8.5000%

b.

i.

Only risky

asset held

Pick stock

with

higher

Sharpe

ratio

Pick stock

with

higher

One of

Pick stock

with

higher

Treynor

measure

Problem 24-09

Consider the two (excess return) index-model regression results for stocks Aand 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)

i.Alpha % %

ii.Information ratio

iii.Sharpe ratio

Inputs:

Act Rtn Act Wt BM Wt Indx Rtn

Equity 0.023 0.5 0.3 0.028 S&P 500

Bonds 0.013 0.4 0.2 0.014 Salomon Indx

Cash 0.005 0.1 0.5 0.005

nce

0.0137

Actual

Performa

nce

0.0172

Difference 0.0035

Answers:

a.1.

The

manager’s

return in

the

month

on of

security

1.72%

Over

Problem 24-11

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 i n

column 2, the benchmark or neutral sector allocations in column 3, and the returns of sector indices in column 4.

Actual Return Actual Weight Benchmark Weight Index Return

Equity 2% 0.70 0.60 2.5% (S&P 500)

a-1.What was the manager’s return in the month? (Do not round intermediate calculations. Input all amounts as positive

values. Round your answer to 2 decimal places. Omit the “%” sign in your response.)

The manager’s return in the month is %

a-2.What was her overperformance or underperformance? (Do not round intermediate calculations. Input all amounts as

positive values. Round your answer to 2 decimal places. Omit the “%” sign in your response.)

Inputs:

Country

Wt MSCI

Indx

Mgr’s Wt

Mgr’s Rtn

in Country

Rtn of Stk

Indx for

that

Country

UK 0.24 0.48 0.21 0.13

Japan 0.37 0.1 0.16 0.16

US 0.36 0.27 0.1 0.12

Germany 0.03 0.15 0.06 0.13

Performan

ce

0.1303

b. Difference -0.0072

c.

Stock

Selection

Contributi

on

0.0225

Answers:

Added

value

1.53%

on of

selection

Contributi

Problem 24-12

A global equity manager is assigned to select stocks from a universe of large stocks throughout the world. The manager will b e evaluated by comparing her returns to

the return on the MSCI 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 Manager’s Return in Country Return of Stock Index for That Country

U.K. 0.15 .30 20% 12%

Japan 0.30 .10 15 15

U.S. 0.45 .40 10 14

Germany 0.10 .20 5 12

Performan

ce

Answer:

Problem 24-16

Bill Smith is evaluating the performance of four large-cap equity portfolios: Funds A, B, C, and D. As part of his analysis, Smith

computed the Sharpe ratio and the Treynor measure for all four funds. Based on his finding, the ranks assigned to the four funds are

as follows:

Fund Treynor Measure Rank Sharpe Ratio Rank

A 1 4

B 2 3

C 3 2

D 4 1

The difference in rankings for Funds A and D is most likely due to:

Inputs:

Weight Return

Style

Mid-Cap

Growth

0.15 0.4 0.24 0.26

Small-Cap

Growth

0.25 0.1 0.2 0.18

Answers:

Large-Cap

Growth

0.60%

Small-Cap

Growth

Problem 24-17

Primo Management Co. is looking at how best to evaluate the performance of its managers. Primo has been hearing

more and more about benchmark portfolios and is interested in trying this approach. As such, the company hired Sally

Weight Return

Style Category Primo Benchmark Primo Benchmark

Large-cap growth 0.60 0.50 17% 16%

Mid-cap growth 0.15 0.40 24 26

Small-cap growth 0.25 0.10 20 18

As part of her analysis, Jones also takes a look at one of Primo’s global funds. In this particular portfolio, Primo is

Small-cap growth %

Total within-sector selection %

Category

Primo

Benchmark

Primo Benchmark

Large-Cap

Growth

0.6 0.5 0.17 0.16

Mid-Cap

Growth

0.15 0.4 0.24 0.26

Primo

Performa

nce

0.188

Benchmar

k

Performa

nce

0.202

Performa

nce

Benchmar

Performa

nce

Security

Selection

Performa

nce

Primo

Sector

Benchmar

k Security

Selection

Performa

nce

0.18

Answers:

Primo out –

(or under)

performa

nce %

-1.40% underperformed

decisions:

Pure

Problem 24-18

Primo Management Co. is looking at how best to evaluate the performance of its managers. Primo has been hearing

more and more about benchmark portfolios and is interested in trying this approach. As such, the company hired

Sally Jones, CFA, as a consultant to educate the managers on the best methods for constructing a benchmark

portfolio, how best to choose a benchmark, whether the style of the fund under management matters, and what

they should do with their global funds in terms of benchmarking.

For the sake of discussion, Jones put together some comparative 2-year performance numbers that relate to Primo’s

current domestic funds under management and a potential benchmark.

Weight Return

Style Category Primo Benchmark Primo Benchmark

As part of her analysis, Jones also takes a look at one of Primo’s global funds. In this particular portfolio, Primo is

invested 75% in Dutch stocks and 25% in British stocks. The benchmark invested 50% in each—Dutch and British

stocks. On average, the British stocks outperformed the Dutch stocks. The euro appreciated 6% versus the U.S. dollar

over the holding period while the pound depreciated 2% versus the dollar. In terms of the local return, Primo

outperformed the benchmark with the Dutch investments, but underperformed the index with respect to the British

stocks.

1.Calculate the amount by which the Primo portfolio out– (or under-) performed the market over the period?

(Round

your answer to 1 decimal place. Input the amount as positive value. Omit the “%” sign in your response.)

Small-Cap

Growth

Inputs:

Small-Cap

Growth

0.25 0.1 0.2 0.18

Primo

Performa

nce

0.188

Performa

nce

Performa

nce

Performa

nce

0.202

Answer:

Primo

Security

Selection

Performa

nce

0.188

k Security

Selection

Performa

nce

A

negative

market

Problem 24-20

Primo Management Co. is looking at how best to evaluate the performance of its managers. Primo has been

hearing more and more about benchmark portfolios and is interested in trying this approach. As such, the

company hired Sally Jones, CFA, as a consultant to educate the managers on the best methods for constructing a

As part of her analysis, Jones also takes a look at one of Primo’s global funds. In this particular portfolio, Primo is

invested 75% in Dutch stocks and 25% in British stocks. The benchmark invested 50% in each—Dutch and British

stocks. On average, the British stocks outperformed the Dutch stocks. The euro appreciated 6% versus the U.S.

dollar over the holding period while the pound depreciated 2% versus the dollar. In terms of the local return,

Primo outperformed the benchmark with the Dutch investments, but underperformed the index with respect to

the British stocks.

Style