FINANCIAL ECONOMICS
boomshaka
RP1_Sp20_03.docxEcon413 RP 1
I Expected Value, Variance and Standard deviation
I.I Stock Analysis
1. Identify and describe your two assets
2. Download the last year daily close prices for your assets using the links provided in the excel
3. Import daily close values into excel and compute
a. Log returns
b. Expected returns – equally likely
c. Variance – theoretical mean zero variance formula
d. Standard deviation- volatility
e. Covariance– theoretical formula and Excel COVAR function
· Determine: positive, negative, or zero covariance
Note: When calculating above statistics, make sure your M (# of variables) is consistent with# of returns
i.e. if you have 10 daily close prices you will have 9 daily returns
II Utility Analysis and Risk Attitudes
II.I A gamble based on a fair coin toss has payoffs described in your excel. (fair coin toss i.e. probability of heads is 50%=probability of tails is 50%)
1. Calculate the Expected value of this gamble
2. Calculate Expected utility(E[U(w)]) and the utility of expected value (U(EV)) for each utility function
· state the relationship >, <, = and classify the risk attitude
II.II A risk agent, whose utility is given by U(w) = 5ln(w) and initial
wealth is $10,000 is faced with a potential loss of $3,500 with a probability
of p= 0.20. What is the maximum premium they would be willing to pay to
protect themselves against this loss? (i.e. probability of earning $0 is (1-p) and probability
of losing $3,500 is 0.20; but think what your opportunities of terminal wealth are)
3. What is the agents risk appetite?
4. Find the expected value
5. Find the expected utility(of wealth)
6. Find the maximum premium(y) to equate
U(wi−y)=E[U(w)]
U (initial wealth−y) =E[U(w)]
Show all your work
7. What if you were given the opportunity to purchase insurance for $450, would you take the insurance? Why
II.III Calculate and classify the following utility functions according to the absolute and relative risk aversion Show all your work
8. U(w)= 250-w
9. U(w)=w-5w2
