FINANCIAL ECONOMICS

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

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

III. Extra Credit: Find on template

I

0

SP500 RIO

on

SP500 RIO

return

CLOSE return r2

ected value(return)

3

-0.014258

SP500

RIO

9/5/19

SP5

0

RIO

N

252

return

Date

CLOSE

r2

retSP-avgSP

retRIO-avgRIO

M

1

Ex

p

9/5/19

1/18/19

2670.709961

51.639999

Variance

1/22/19

2632.899902

-0.014258

0.000

20

50.310001

sd

1/23/19

1/24/19

Cov formula

1/25/19

COVAR function

1/28/19

1/29/19

1/30/19

Asset Summary

Asset type

Sector

Industry

Exchange

1/31/19

Matrix

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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

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

__U(EV)

u(w)

EU__U(EV)

u(w)

EU__U(EV)

is faced with a potential loss of $3,500 with a probability

p

EV

0

EU 10,000

250-w u(w)

u'(w)

u”(w)

A'(w)

R'(w)

A'(w)

R'(w)

A gamble based on a fair coin toss which pays $	250
	EV
E[U(w)]	U[EV]	> < =	risk attitude
		u(w)	5ln(w)				EU
5w2
	250-w
A risk agent, whose utility is given by U(w) = 5ln(w) and initial
wealth is $	10,000
of p= 0.20. What is the maximum premium they would be willing to pay to
protect themselves against this loss?
risk appetite	wT
intial wealth
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)	w-5w2
	u'(w)
	u”(w)
		A'(w)
		R'(w)
A(w)	A(w) =
A'(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?