An entity has a stock that has a beta of 1.20 when the risk free rate is 5% in 2
ID: 2774266 • Letter: A
Question
An entity has a stock that has a beta of 1.20 when the risk free rate is 5% in 2010. The average return on the market in 2010 was 12%. In 2011 the risk free rate increased by 1% due to inflation, but the return on the market increased by 2%.
However, in 2012 the rate of inflation slowed and the risk free rate and the market return were the same as in 2011. In the year 2013, the return on the market decreased to 14% and the risk free rate to 7%, beta was increased to 1.50.
Required:
a. Calculate the yearly return on the stock using CAPM
b. Calculate the average return on the stock
c. Calculate the standard deviation of the returns
Explanation / Answer
a. We have :
Year 2010
Beta = 1.2
Rf =5%
Rm = 12%
Return = Rf +(Rm-Rf)beta
= 5% + (12%-5%)x1.2
=13.40%
Year 2011
Beta = 1.2
Rf =6%
Rm = 14%
Return = Rf +(Rm-Rf)beta
= 6% + (14%-6%)x1.2
=15.60%
Year 2012
Beta = 1.2
Rf =6%
Rm = 14%
Return = Rf +(Rm-Rf)beta
= 6% + (14%-6%)x1.2
=15.60%
Year 2013
Beta = 1.5
Rf =7%
Rm = 14%
Return = Rf +(Rm-Rf)beta
= 7% + (14%-7%)x1.5
=17.50%
b.
Year Return
2010 13.40%
2011 15.60%
2012 15.60%
2013 17.50%
Total 62.10%
Average return = sum of returns/ no.of years
= 62.10%/4
=15.525%
c.
Year R R-AR (R-AR)^2
2010 13.40% -2.125 4.5156
2011 15.60 0.075 0.005625
2012 15.60 0.075 0.005625
2013 17.50 1.975 3.900625
8.4275
Variance = sum of (R-AR)^2/(n-1)
=8.4275/(4-1)
= 2.81
Standard deviation = variance ^.5
=2.81^0.50
=1.676%