Practice Problems (Risk and Return)
1. Your stock had the following returns in the four quarters of a given year: +8%, -5%, +6%,
+4%.
Required:
a. Find out holding period return.
b. Find out the mean return for one quarter (Geometric Mean).
c. How did it compare against the benchmark index, which had total returns of 12% over
the year?
d. Find out the discrete annualized return
e. Find out the continuous holding period return.
f. Find out the continuous mean return.
g. Find out the continuous annualized return.
2. Let an investment had initial value of $2,50,000. The value of the investment after 10 years
is $3,00,000.
a. Find out the holding period return.
b. Find out the mean return (use geometric mean).
3. A stock had initial value of $30 and the value of the stock after 2 years is $ 35. The stock
has paid dividend of $10.
a. Find out the capital gain yield.
b. Find out the dividend yield.
c. Find out the holding period return.
d. Find out the mean return for one year (use geometric mean).
4. A stock’s initial value was $ 15 and the value after two years is $25.
a. Find out the holding period return.
b. Find out the mean return (geometric mean).
c. If inflation rate is 3%, find out the real rate of return.
5. A stocks day wise return for 10 days is given below:
Day
Price ($)
1
20
2
19
3
22
4
27
5
29
6
29
7
31
8
34
9
37
10
39
a. Find out day wise holding period return.
b. Find out the mean return.
c. Find out the annualized return.
t
 ln(1  HPR )
[Note: Continuous Mean Return  i 1
i
t
, HPRi  Discrete holding period return]
t
P
d. Show that, HPR*   ln(1  HPRi )  ln( t ) numerically using stock price data [ HPR* 
P0
i 1
Continuous holding period return].
6. Let a stock has returns of 5%, 8%, 9%, 10%,15% in five consecutive periods.
a. Find out the expected return.
b. Find out the risk.
c. If the inflation is 5%, find out the real return.
7. Let a stock will have returns of 5%, 8%, 9%, 10%, 15% in five consecutive periods and
their corresponding probabilities are 10%, 20%, 5%, 5%, 50%.
a. Find out the expected return.
b. Find out the risk.
c. If the inflation is 5%, find out the real return.