02 Jun Question I.I SP500 & XOM (Sep 16,2013 – Sep 14,2014)
Question
I.I
SP500 & XOM (Sep 16,2013 – Sep 14,2014)
(30 pt)
1. Download the last year daily close prices for SP500 index from yahoo finance
a. http://finance.yahoo.com/q?s=%5EGSPC
2. Download the last year daily close prices for ExxonMobil (XOM) from yahoo finance
a. http://finance.yahoo.com/q?s=XOM
3. Import daily close values into excel and compute
a. Log return
b. Expected return
c. Variance – mean zero theoretical formula
d. Standard Deviation
e. Covariance – theoretical formula and the COVAR excel function
i. Comment on the covariance you computed
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 which pays $45 if the coin lands heads and $32 if the coin
lands tails. ( fair coin toss i.e. probability of heads is 50% = probability of tails is 50%)
(30 pt)
1. Calculate the Expected value of this gamble
2. Calculate Expected utility function
a. u(w) = 8w classify the risk attitude
b. u(w) = ln(w) classify the risk attitude
c. u(w) = 2w2 classify the risk attitude
II.II
A risk averse agent, whose utility is given by u(x) = ln x and wealth is $50, 000 is faced with a
potential loss of $10, 000 with a probability of p = 0.1. What is the maximum premium they would be
willing to pay to protect themselves against this loss? ( i.e. probability of earning 0 is 0.9 and probability
of losing 10,000 is 0.1)
(25 pt)
1. Find expected value
2. Find the expected utility (of wealth)
3. Find the maximum premium to equate the two
???? ? ??? = ??[???????]
4. Compare the maximum risk premium (y) to the expected loss ( wealth – expected value)
II.III
Calculate and classify the following utility functions according to the absolute and relative risk
aversion
(15 pt)
1. u(w) =ln(w)
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