A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 5.5%. The probability distribution of the risky funds is as follows: Expected Return Standard Deviation
Stock fund (S) 15% 32%
Bond fund (B) 9 23

The correlation between the fund returns is 0.15.

Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations and round your final answers to 2 decimal places. Omit the "%" sign in your response.)

Portfolio invested in the stock %
Portfolio invested in the bond %
Expected return %
Standard deviation %
rev: 11_21_2013_QC_39542

Explanation:

The parameters of the opportunity set are:
E(rS) = 15%, E(rB) = 9%, σS = 32%, σB = 23%, rho = 0.15, rf = 5.5%
From the standard deviations and the correlation coefficient we generate the covariance matrix [note that Cov(rS, rB) = rhoσSσB]:

Bonds Stocks
Bonds 529.0 110.4
Stocks 110.4 1,024.0
The optimal risky portfolio proportions are:
wB =
[E(rB) − rf ]σS2 − [E(rS) − rf ]σBσSrhoBS

[E(rB) − rf ]σS2 + [E(rS) − rf ]σB2 − [E(rB) − rf + E(rS) − rf ]σBσSrhoBS
wB =
(((0.09 − 0.055) × 0.1024) − (0.15 − 0.055) × (0.01104))

(((0.09 − 0.055) × 0.1024) + (0.15 − 0.055) × 0.0529) − ((0.09 − 0.055 + 0.15 − 0.055) × 0.01104)
= 0.3534 = 35.34%
wS = 1 − wB
wS = 1 − 0.3534 = 0.6466 = 64.66%
The mean and standard deviation of the optimal risky portfolio are:
E(r) = wB × E(rB) wS × E(rS)
= (0.3534 × 0.09) + (0.6466 × 0.15)
= 0.1288 = 12.88%
SD(r) = [wS2σS2 + wB2σB2 + 2wSwB Cov(rS, rB)]1/2
= [(0.64662 × 0.322) + (0.35342 × 0.232) + (2 × 0.6466 × 0.3534 × 0.01104))]1/2
= 0.2334 = 23.34%.

can someone explain to me where is this .01104 coming from?? and what are these 529 110.4 110.4 1024.0 in the middle? how to get these?