Problem 6-7 Consider the following table: Calculate the values of mean return an
ID: 2712852 • Letter: P
Question
Problem 6-7
Consider the following table:
Calculate the values of mean return and variance for the stock fund. (Do not round intermediate calculations. Round "Mean return" value to 1 decimal place and "Variance" to 4 decimal places.)
Calculate the value of the covariance between the stock and bond funds. (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 4 decimal places.)
rev: 10_11_2013_QC_37085
Consider the following table:
Explanation / Answer
Answer (a)
Mean return of stock fund = 10.6%
Standard Deviation of stock fund = 31.75%
Answer (b)
Covariance between stock fund and bond fund = 0.0079
Probability (p)
Stock Fund
Bond Fund
Rate of return (r)
p*r
Rate of return (r)
p*r
0.10
-46%
-4.6%
-20%
-2.00%
0.20
-24%
-4.8%
14%
2.80%
0.30
8%
2.4%
5%
1.50%
0.40
44%
17.6%
5%
2.00%
Mean return (e(r))
10.6%
4.3%
Variance of stock fund = 0.1 * (-0.46 – 0.106)^2 + 0.2 * (-0.24-0.106)^2 + 0.3 * (0.08-0.106)^2 + 0.4 * (0.44 – 0.106)62
Variance = 0.1 * (-0.566)^2 + 0.2 * (-0.346)^2 + 0.3 * (-0.026)^2 + 0.4 * (0.334)^2
Variance = 0.1 * 0.320356 + 0.2 * 0.119716 + 0.3 *0.000676 + 0.4 * 0.111556
Variance = 0.0320356 + 0.0239432 + 0.0002028 + 0.0446224
Variance = 0.100804
Standard Deviation = Square root (0.100804) = 0.317496 or 31.75% (rounded off)
Covariance between stock and bond funds = Sum of (probability *[(stock return – mean)] *(bond return – mean)]]
Covariance = [0.1 * (-0.46-0.106)*(-0.20-0.043) + [0.2 * (-0.24-0.106)]*(0.14-0.043)] + [0.3 * (0.08-0.106)]*(0.05-0.043)] + [0.4 * (0.44-0.106)]*(0.05-0.043)
Covariance = 0.1 * -0.566 * -0.243 + 0.2 * -0.346 * 0.097 + 0.3 * -0.026 * 0.007 + 0.4 * 0.334 * 0.007
= 0.0137538 - 0.0067124 - 0.0000546+ 0.0009352
= 0.007922 or 0.0079 (rounded off)
Probability (p)
Stock Fund
Bond Fund
Rate of return (r)
p*r
Rate of return (r)
p*r
0.10
-46%
-4.6%
-20%
-2.00%
0.20
-24%
-4.8%
14%
2.80%
0.30
8%
2.4%
5%
1.50%
0.40
44%
17.6%
5%
2.00%
Mean return (e(r))
10.6%
4.3%