Portfolio Management

Portfolio Management

TABLE OF CONTENTS
Question 1..............................................................................................................................3
Question 2..............................................................................................................................4
Question 3..............................................................................................................................5
REFERENCES...........................................................................................................................8

Question 1
A.
First, solve for the expected return of asset X:
Expected return on risk free asset = 9.5% = 0.5 * 4% + 0.5 *(Expected return on risky asset
X)
Expected return on risky asset X= (9.5% - 2%) / 0.5 = 15%.
The portfolio having the 20% risk free and 80% invested into riskier asset X has the expected
return of = 0.2 * 4% + 0.8 * 15% = 12.8%.
All the combination s will lie on the same line irrespective of the fact whether they are riskier
or risk free, therefore, they will have Sharpe ratio. Thus, Sharpe ratio will still remain the
same, thus, the standard deviation of the portfolio return with the revised weights is computed
below.
0.3667 = 0.128 -0.04 / σp
σp = 0.088 / 0.3667 = 0.240 = 24%
B.
There is an equation for the variance pertaining to the portfolio in regard to the assets and
covariance with the entire portfolio. In this, xi is the proportion of the portfolio invested in the
asset i.
Var (Rp) = ∑ xi Cov (Ri Rp).
Since, standard deviation is the square root of the variance, thus, the standard deviation will
be calculated as follows.
Standard deviation = Square root of [(40000 / 100000) * 0.15 + (20000 / 100000) * (-0.10) +
(10000 / 100000) * 0.20 + (30000 / 100000) * (-0.05)]
= 21.2%
C.
(i)
The present value of annuity refers to the current value of the future expected cash flows at a
particular rate also called as the discounting rate. Higher is eth discount rate, the less is the