You invest equal sums (lets say $1000 and $1000) into blue chip shares and penny stock. And worry about the volatility of your portfolio. The table below lists the probabilities of getting certain values of returns:

Return on penny stocks, $	Probability		Return on blue chips, $	Probability
-10	0.3		-10	0.1
10	0.2		10	0.7
30	0.5		30	0.2

For penny stocks, the mean return is P=$4.67 and the variance is P2=$2130.37 . For blue chips, they are B=$4.00 and B2=$260.00 .

1. Compose the joint probability table for obtaining the returns of $-10, 10, and 30 on blue chips and the same values on penny stocks. Treat the two variables as independent. For examples, refer to Table 5.8 .

Saratoga Dealership.

Geneva Dealership	0	1	2	3	4	5	Total
0	.0700	.1000	.0800	.0300	.0067	.000	.2867
1	.0700	.1200	.1100	.0600	.0067	.0033	.3700
2	.0300	.1400	.0300	.0400	.0100	.0067	.2567
3	.0100	.0300	.0200	.0100	.0167	.0000	.0867
Total	.18	.39	.24	.14	.04	.01	1.0000

Fig: Table 5.8

(b) Add up the values in the joint table to obtain the probabilities of your portfolio generating returns of $-20, 0, 20, 40, and $60.

(c) Find the mean and variance of your total portfolio return, P+B and P+B2 .

(d) Use the square of the sum formula (5.6 in book) for bivariate variance to find the covariance, PB .

(e) Now suppose you want to reduce the volatility of your portfolio, even if at the cost of the expected return. You want to only have a=0.67 in your penny stocks and as much as b=1.33 in your blue chips (that would make it $667 and $1333, given that you started with a $1000 and a $1000, but this is irrelevant for your calculation).

Use the linear combination formula to find the variance of your new portfolio, aP+bB2