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25 against 0.5) and the probability of favorable outcome is 0.75 compared to 0.5 for a one company stock portfolio.
A d) Calculate the probability that you will end up with nothing, and the probability that you will end up with $210,000, for each of the following cases: splitting your money evenly between 3 stocks, between 5 stocks, and between 10 stocks. What is happening to the probability of "in-between" outcomes as portfolio diversification increases in this example (no exact answer required, just tell me whether the likelihood of in-between outcomes is going up or going down)?
Answer: probability for 3 stocks of ending with 0 and ending with 210,000 is equal to 0.5*(1/3)=1/6
For 5 stocks ending with 0 and ending with 210,000 is equal to 0.5*(1/5)=1/10
For 10 stocks ending with 0 and ending with 210,000 is equal to 0.5*(1/10)=1/20
The probability of in-between outcomes is growing as it can be found as total probability minus probability of ending with 0 and ending with 210,000:
e) in this example, more diversification is always better -- if there are a million stocks available then your best strategy would be to buy a tiny amount of each. But now suppose there is a fixed brokerage fee of, say, $10 for each company's stock that you purchased, independent of how many shares you purchased, so that if you bought shares in a million companies you'd have to pay the $10 fee a million times. How would that affect your optimal degree of...
b) What is the standard deviation of Stock a and B?
A standard deviation for stock a:
x|=?.3*(2.3+1)^2+.3*(2.3-2)^2+.4*(2.3-5)^2 x|=2.49% standard deviation for stock B:
x|=?.3*(2.8+2)^2+.2*(2.8-2)^2+.5*(2.8-6)^2 x|=3.48% c) if both Stock a and Stock B. have the same supply, which stock will sell at a higher price? Why?
Answer: Stock a will have a higher price as it has smaller standard deviation. Even though that expected return is pretty much similar for both stocks (2.3% for stock a and 2.8% for stock B), standard deviation of stock B. is 1% bigger, meaning…
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