Calculation completed..need help understanding.

A venture capital fund has the mandate to invest in new businesses that may be perceived as being too risky by other investors. Suppose that a fund invests its funds in units with no more than one unit per firm in order to diversify its investments. Furthermore, suppose there are two classes of firms with the following distributions of net returns, and assume that all firms operate independently of each other.
Type A firm
% returns -15 0 45
Probability .30 .30 .40
Type B firm
% returns 0 25 65
Probablity .30 .20

a.) Both firms have the same expected return. Compute and interpret it. (How do I interpret it the following data)

Expected return= E(X)=sigma XP(X)=13.5

variance=695.25

Standard deviation of the return=26.3676

b.) Suppose that a single investor has only one and only one unit to invest. Which type of firm would the investor prefer to invest in and why?

C.)Suppose the venture fund has 100 units to invest. If it decides to invest them ALL in Type A firms, find the expected average return on ALL 100 investments and compute its standard deviation.

E(100X)=100xE(X)=100x13.5=1350

variance=6952500

standard deviation of the average return on all 100 investments=2636.76

d.) Between b and c above which would be more likely to yield the expected return? Why?

Question

Calculation completed..need help understanding.

A venture capital fund has the mandate to invest in new businesses that may be perceived as being too risky by other investors. Suppose that a fund invests its funds in units with no more than one unit per firm in order to diversify its investments. Furthermore, suppose there are two classes of firms with the following distributions of net returns, and assume that all firms operate independently of each other.
Type A firm			
% returns	-15	0	45
Probability	.30	.30	.40
Type B firm			
% returns	0	25	65
Probablity	.30	.20

a.)   Both firms have the same expected return. Compute and interpret it. (How do I interpret it the following data)

Expected return= E(X)=sigma XP(X)=13.5

variance=695.25

Standard deviation of the return=26.3676

b.)   Suppose that a single investor has only one and only one unit to invest. Which type of firm would the investor prefer to invest in and why?

C.)Suppose the venture fund has 100 units to invest. If it decides to invest them ALL in Type A firms, find the expected average return on ALL 100 investments and compute its standard deviation.

E(100X)=100xE(X)=100x13.5=1350

variance=6952500

standard deviation of the average return on all 100 investments=2636.76

d.)   Between b and c above which would be more likely to yield the expected return? Why?

kirbykirby · Answer

Well the expected return tells you how much money you'd make in the long run investing in firm A or B. So, you'd expected to hopefully get a gain of +13.5 by investing in firm A or B. However, this refers to a long run (theoretically infinite) average, so in the short term, you may experience a loss or a gain, but investing in the firm for a long term should earn you something close to 13.5 

Now since both firms have the same expected return, it would probably be wise to invest in the firm that has the lowest variance, that is it has the lowest variability. That is because it would be a safer bet to invest in the firm that would be more guaranteed to expect your +13.5 return, but if it's more variable, then there might be a chance to lose a lot (although you can argue that there is a higher chance to gain more too..., but the risk of loss might be too great)