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FINANCIAL ECONOMICS DISCUSSION ASSIGNMENT

FINANCIAL ECONOMICS DISCUSSION ASSIGNMENT

Read the document for the questions and you are to complete all of your work including written answers and calculations on the excel template provided.

Econ413 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

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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? FINANCIAL ECONOMICS DISCUSSION ASSIGNMENT

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

III. Extra Credit: Find on template

SP500 RIO N 252 SP500 RIO return on SP500 RIO
Date CLOSE return r2 retSP-avgSP CLOSE return r2 retRIO-avgRIO M 1 Expected value(return) 9/5/19
1/18/19 2670.709961 51.639999 Variance
1/22/19 2632.899902 -0.014258 0.000203 -0.014258 50.310001 sd
1/23/19
1/24/19 Cov formula
1/25/19 COVAR function
1/28/19
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1/30/19 Asset Summary Asset type Sector Industry Exchange
1/31/19 Matrix
2/1/19 SP500
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2/8/19 RIO
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2/19/19 hint use the profile tab under yahoo finance for each asset
2/20/19 Asset type: Stock / Bond / ETF / Currency / Mutual Fund / Index
2/21/19 Exchange: NYSE, NASDAQ, LSE, Euronext, ASX, SEHK.. Etc
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https://finance.yahoo.com/quote/%5EGSPC/history?p=%5EGSPC https://finance.yahoo.com/quote/RIO/history

II

A gamble based on a fair coin toss which pays $250 if the coin lands heads and $20 if the coin lands tails. ( fair coin toss i.e. probability of heads is 50% = probability of tails is 50%)
250 20
EV
E[U(w)] U[EV] > < = risk attitude
u(w) 5ln(w) EU__U(EV)
u(w) 5w2 EU__U(EV)
u(w) 250-w EU__U(EV)
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? FINANCIAL ECONOMICS DISCUSSION ASSIGNMENT
risk appetite wT p
EV intial wealth 0
EU 10,000
U(w-y) = E[U(w)] -3,500
5ln(10,000-y)=B17
find y
y= If you are given the opportunity to buy insurance for $450
alt y = would you take the insurance?
Utility functions w>0
quad b>0
u(w) 250-w u(w) w-5w2
u'(w) u'(w)
u”(w) u”(w)
A'(w) A'(w)
R'(w) R'(w)
A(w) A(w) =
A'(w) A'(w) =
R(w) R(w)=
R'(w) R'(w) =

Extra

What is the difference between QE and Open market Operations (OMO)?
What is a repo agreement? And why does the Fed construct these repos?
Why did the Fed issue $82B in financial markets in Jan 2020?

FINANCIAL ECONOMICS DISCUSSION ASSIGNMENT