1. Consider the following limit order book of a specialist in a market that allows partial execution of orders. The last trade in the stock took place at a... [Show More] price of $35.
Bid Bid Qty Ask Qty Ask
34.75 100 800 35.25
34.25 100 1,000 35.50
33.50 400 2,000 35.75
32.25 200 800 36.00
You place a market sell order for 150 shares. What are your proceeds and what is the new stock price?
2. An investor invests 40% of his wealth in a risky asset with an expected rate of return of 15% and a variance of 4% and 60% in a treasury bill that pays 6%. What is the portfolio’s standard deviation?
3. For the aggregate U.S. stock market,
A) daily returns are very predictable
B) daily squared returns are very predictable
C) daily squared returns are positively autocorrelated
D) daily squared returns are negatively autocorrelated
E) B and D
F) B and C
4. Which of the following portfolios cannot be on the efficient frontier?
Portfolio Expected Return Standard Deviation
I 8% 10%
J 16% 20%
K 15% 25%
L 25% 38%
A) Portfolio I
B) Portfolio J
C) Portfolio K
D) Portfolio L
E) Cannot be determined
5. Market timing is possible based on which of the following asset allocation rules / portfo- lios? (circle the ones that are correct)
A) minimum variance portfolio
B) risk parity
C) 1/N
D) all of the above
E) tangency portfolio
6. A coupon bond which pays interest of $50 annually, has a par value of $1,000, matures in 2 years, and is selling today at $991.50. The current yield on this bond is .
A) 4.34%
B) 4.76%
C) 5.00%
D) 5.46%
E) 5.94%
7. Suppose the Capital Asset Pricing Model (CAPM) assumptions hold. The market port- folio consists of only 2 risky assets, which are in positive net supply. The expected rate of return of assets A and B are 10% and 13% respectively, their market betas are 0.5 and
0.8 respectively, and the risk free rate is 5%. Is this economy in equilibrium?
A) Yes, both assets lie on the SML, satisfying the optimality of the market.
B) No, asset A is held in negative amount in the tangency portfolio in contrast to supply=demand condition.
C) No, asset B is held in negative amount in the tangency portfolio in contrast to supply=demand condition.
D) It is impossible to tell without further information about the correlation between the two assets
E) None of the above
8. A put option is more valuable when
A) it has more time to maturity and when it has a higher strike price
B) it has more time to maturity and when it has a lower strike price
C) it has less time to maturity and when it has a higher strike price
D) it has less time to maturity and when it has a lower strike price
E) none of the above
1. When backtesting risk parity portfolios based on on an investment universe that includes both bonds and stocks over 1980 to 2014, one finds that the strategy produces a higher Sharpe ratio than the naive 1/N strategy. Explain why this is the case.
2. In the context of the CAPM, what is meant by the term ’anomaly’? Give an example of a market anomaly and explain why it is considered to be an anomaly.
3. True or False (Explain): Two assets that have identical cash flows must have the same price.
4. You regress monthly excess returns on Funny Fund onto the four Carhart factors and a constant, i.e. you estimate the time series regression
re = α + βM • re
+ βSMB • rSMB,t + βHML • rHML,t + βWML • rWML,t + ϵt
and you obtain the parameter estimates αˆ = 0.005 (t-stat=0.6), βˆM = 0.97 (t-stat=2.1), βˆSM B = 0.43 (t-stat=2.9), βˆHM L = 0.08 (t-stat=-1.3), and βˆW ML = 0.70 (t-stat=3.1). What investment style does Funny fund follow, i.e. what types of stocks does it tend to
buy?
1. A $100 par, 6% annual coupon bond that matures in 1 year currently trades at $95.40, and a $100 par, 4% annual coupon bond with two years left until maturity trades at
$95.12.
(a) What are the 1- and 2-year discount factors?
(b) What is the value of a 2-year annuity paying $100 each year?
(c) What is the forward rate from year 1 to year 2?
2. Returns of all assets in the economy are exposed to two risk factors, f1 and f2. Both factors have mean zero, i.e. E[f1] = E[f2] = 0. Furthermore, a very large number of each of three types of assets is traded, whose returns are given by
rA,i =0.04 + 2f1 − 2f2 + εA,i rB,i =0.03 − 1f1 + 2f2 + εB,i rC,i =0.11 + 3f1 + εC,i
The ε’s represent purely idiosyncratic risk, i.e. they are uncorrelated across individual assets of all three types. For example, assets of type A differ only in terms of their idiosyncratic returns εA,i, but not in terms of their mean returns or factor exposures.
(a) Find the pure factor portfolio for the first factor and its expected return.
(b) Under no arbitrage, what is the risk-free rate in the economy?
(c) Under no arbitrage, what is the expected return of an asset with loading 2 on factor one and loading 0 on factor two?
3. Securities A and B are perfectly correlated. The standard deviation of the returns on A and B is 15% and 10% respectively. The means are 7% and 5% respectively. Assume the risk free rate is 3%.
(a) Describe in detail the portfolio of the two securities with the lowest possible risk (weights, expected return, standard deviation)
(b) Is there an arbitrage opportunity? If yes, describe the arbitrage portfolio. If no, explain why the observed prices can persist. [Show Less]
