Answer:
<em>a) Weight of Assets: </em>
<em>Stock A = 0.33</em>
<em>Stock B = 0.18</em>
<em>Stock C = 0.35</em>
<em>Stock D = 0.13</em>
<em>b) Geometric Average Return = 8.1%</em>
<em>c) Risk free rate (without inflation rate adjustment) = 6.4%</em>
<em>Risk free rate (with inflation rate adjustment) = 3.4%</em>
<em>d) As, this part is incomplete and missing essential data, so we have skipped this part. </em>
Step-by-step explanation:
a) Weights of the assets:
Weights of the assets in Rachel's portfolio can be calculated as follows:
Weight = Amount in stock/sum of amounts of all stocks
Sum of amount of all stocks = Stock A + Stock B + Stock C + Stock D
= $13500 + $7600 + $14700 + $5,500
Sum = $41,300
Weight of Stock A = .Amount of Stock A/ Sum
= 13600/41300
Weight of Stock A = 0.329 ≈ 0.33
Weight of Stock B = 7600/41300
= 0.18
Weight of Stock C = 14700/41300
= 0.35
Weight of Stock D = 5500/41300
= 0.13
b) Geometric Average Return:
The formula to calculate geometric average return is as follows:
<em>Geometric average return = ((1+r1)x(1+r2)x(1+r3)....x(1+rn))^(1/n) - 1</em>
Don't be confuse! This is a very simple formula, it only looks complex. Just plug in the values of returns given for this portfolio to get the geometric average return.
Here we go:
Geometric Avg. Return = ((1+0.097)*(1+0.124)*(1-0.055)*(1+0.172))^(1/4) - 1
<em>Geometric Avg. Return = 0.081 = 8.1% </em>
<em></em>
c) Risk Free Rate using CAPM:
<em>CAPM = Capital Asset Pricing Model</em>
CAPM gives the formula to calculate risk free rate:
Expected Return = Risk Free rate + (Beta of the stock x Premium Risk)
: As this is without the adjustment of inflation rates.
13.6 = Risk Free Rate + (1.5 x 4.8)
Risk Free Rate = 13.6 - 7.2
Risk Free Rate (without inflation adjustment) = 6.4%
With inflation adjustment of Return rate = ((1+r)/(1+IR))-1
Where, r = return, IR = inflation rate
With inflation adjustment of Return rate = ((1+r)/(1+IR))-1
= ((1+0.136)/(1+0.027))-1
Return rate (with inflation rate) = 0.106 = 10.6%
Now, again using CAPM to get risk free rate with inflation rate adjustment.
Expected Return = Risk Free rate + (Beta of the stock x Premium Risk)
10.6% = Risk free rate + (1.5 x 4.8)
Risk Free Rate = 10.6 - 7.2
<em>Risk Free rate = 3.4</em>
