Using the data from Table 12.3 , what is the volatility of an equally weighted p
ID: 2794936 • Letter: U
Question
Using the data from Table 12.3 , what is the volatility of an equally weighted portfolio of Microsoft and Starbucks stock? Data Table Standard Microsoft Starbucks Netflx Coca-Cola McDonald's Clsco Boelng Deviation 25% 61% 16% 14% Microsoft0.35 0.18 0.40 0.430.52 0.28 0.48 0.10 0.34 0.37 0.46 0.19 0.23 0.00 0.35 0.18 0.40 0.43 0.52 0.19 0.23 0.17 0.52 0.17 0.13 0.59 0.10 0.00 0.13 0.10 Coca-Cola 0.59 0.27 0.28 0.28 Boeing Source: Authors' calculations based on data from The Center for Research Iin Security Prices 0.28 0.48 0.10 0.34 0.370.461Explanation / Answer
Volatility of portfolio
The following are the given respective details of the stocks:
Stocks
Volatility
Weight
Microsoft
25%
50%
Starbucks
29%
50%
*Weights assigned is 50% each because each stock is equally weighted.
Now, we required to calculate volatility of portfolio (Microsoft and Starbucks) i.e P
Formula for volatility of portfolio:
P = (m2 x wm2 + s2 x ws2 + 2 x ms x m x wm x s x ws)0.5
The above formula is standard formula for calculating volatility of two asset portfolio
Notations:
P = Volatility of portfolio =?
m = Volatility of Microsoft = 25%
wm = Weight of Microsoft = 50%
s = Volatility of Starbucks = 29%
ws = Weight of Starbucks = 50%
ms = Correlation between Microsoft and Starbucks = +1 (assuming it +1)
Hence, we can solve,
P = (25%2 x 50%2 + 29%2 x 50%2 + 2 x 1 x 25% x 50% x 29% x 50%)0.5
Therefore,
P = 27.00%
Hence volatility of portfolio is 27% at correlation of 1 (or 100%).
Logical check: Average of Microsoft and Starbucks volatility is 27% [(25%+29%)/2]. This simple averaging only holds when you have portfolio of equal weights and correlation of +1
We can solve question for correlation of +0.35 or 35%
P = (25%2 x 50%2 + 29%2 x 50%2 + 2 x 0.35 x 25% x 50% x 29% x 50%)0.5
Therefore, the volatility of portfolio at 35% is:
P = 22.21%
Additional: Working for Volatility at different correlation from -1 to +1 by applying same formula but changing correlation:
Correlation
SD of Portfolio
1.00
27.00%
0.95
26.66%
0.90
26.32%
0.85
25.97%
0.80
25.62%
0.75
25.27%
0.70
24.90%
0.65
24.54%
0.60
24.17%
0.55
23.79%
0.50
23.40%
0.45
23.01%
0.40
22.62%
0.35
22.21%
0.30
21.80%
0.25
21.38%
0.20
20.95%
0.15
20.52%
0.10
20.07%
0.05
19.61%
0.00
19.14%
-0.05
18.66%
-0.10
18.17%
-0.15
17.67%
-0.20
17.15%
-0.25
16.61%
-0.30
16.05%
-0.35
15.48%
-0.40
14.88%
-0.45
14.26%
-0.50
13.61%
-0.55
12.93%
-0.60
12.21%
-0.65
11.44%
-0.70
10.62%
-0.75
9.73%
-0.80
8.75%
-0.85
7.64%
-0.90
6.34%
-0.95
4.70%
-1.00
2.00%
** As correlation is getting reduced from +1 to -1 the volatility of portfolio is also getting reduced or lowering down. This states diversification benefit of the portfolio.
Stocks
Volatility
Weight
Microsoft
25%
50%
Starbucks
29%
50%
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