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Investment Analysis and Portfolio Management

Christmas Worksheet 2009

1. Assume there are two risky stocks available. Stock Ahas an expected return

of 12% and a standard deviation of 8%. Stock Bhas an expected return of 10%and a standard deviation of %.

a. Assumin! the returns on the two stocks are uncorrelated" calculate the

expected return and deviation of the portfolios consistin! of#

i. .=AX " ii. 0=AX " iii. 2.0=AX " iv. .0=AX " v. $.0=AX vi. 1=AX .

b. sin! the answers to &a'" sketch the frontier of returns" the set of efficient

portfolios and mark on the minimum variance portfolio.

c. (f all investors are risk averse" will short sales of either stock be observed)

2. *ow introduce borrowin! and lendin! at a risk+free rate of interest of %.

a. (llustrate the new efficient frontier.

b. ,etermine the structure of the market portfolio.

c. -ow will an increase in the rate of interest affect the percenta!e of stock Ain

the market portfolio)

. i. /hat is the market model and how is the beta of a stock interpreted)

ii. -ow are historic betas calculated)

Assume there are two stocks" Aand B" with 2.1=A and .0=B " and

indiosyncratic variations 2"3 == eBeA .

iii. (f assets Aand Bare the only risky assets available" what must be their

proportions in the market portfolio)

iv. *ow assume that there are other risky assets available and that the risk+free

rate of return is %. (f the mean return on the market portfolio is 8=Mr % and

the variance is 22 =M

" calculate the mean return and variance of a portfolio

consistin! of $0% of stock Aand 0% of stock B.

v. /hat is the mean return and variance of the portfolio in &iv' if

a. (t is 0% financed by borrowin!)

b. (t is financed entirely by borrowin!)

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3. i. Assume that there are available two risky assets. ,escribe the efficient set when

the correlation of their returns is#

a. 4 1

b. 5 1

c. 0.

ii. (f the correlation is 6ero" show how the efficient set is modified when a risk+

free asset is available.

ii. 7or case &ii'" describe the portfolio choice of a risk+averse investor.

iii. -ow are the answers to &ii' and &iii' modified when the rate of interest for

borrowin! is !reater than that for lendin!)

. i. ,efine the sin!le index model. -ow does it differ from the A9:)

ii. ;ou have estimated a beta of 1.2 for :