ECON6029 Financial Economics and Asset Pricing SEMESTER 1 EXAMINATIONS 2021-22
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SEMESTER 1 EXAMINATIONS 2021-22
ECON6029 Financial Economics and Asset Pricing
Section A
A1 Capital Asset Pricing Model and Arbitrage Pricing Theory. [30]
(a) Suppose that an investor with preferences G(uP ; 7P(2)) = uP - a7 P(2) : a > 0 optimally chooses a portfolio composed of only two assets: a single risky asset with expected return uj and variance of return 7j(2) ; and a risk-free asset which yields r0 . Denote by q the proportion of the portfolio invested in the risky asset, and by uP = quj + (1 - q)r0 the expected return on the portfolio. Af- ter deriving the expression for the portfolio risk-return trade-o§, derive the investorís optimal proportion of initial wealth invested in the risky asset. [8]
(b) Now assume that the asset market is frictionless and investors can freely borrow or lend at a risk-free rate, but that they are constrained to invest in portfolios that íblendíthe riskless asset and one risky asset. Suppose that in equilibrium, the only two available risky assets yield uj = 0:12 with a standard deviation of
7j = 0:16 and ul = 0:06 with a standard deviation of 7l = 0:08: What is the risk-free rate of interest in this market? If the investor wishes to hold a portfolio with a standard deviation of 0:10, how should s/he optimally allocate her/his initial wealth? [8]
(c) If the Beta of asset l is 0.8, what are (i) the Beta of asset j, and (ii) the expected return uM and standard deviation 7M of the market portfolio? And (iii) what are the covariances of assets j and l with the market portfolio? [8]
(d) Suppose now that the matrix of asset payo§s is as follows:
0 j
State 1 5 15
State 2 5 8 Price p0 pj
Assets
l
10
7
pl
If the probability of states is the same, write the CAPM in terms of asset prices, and obtain p0 ; pj and pl : At those prices, are there arbitrage oportunities? [6]
A2 Expected Utility and Portfolio Choice. [30]
(a) Under which conditions does the Expected Utility (EU) hypoth- esis hold within the State-Preference approach? Explain why Expected Utility is a particular case of the State-Preference ap- proach. [8]
(b) DeÖne risk aversion and the coe¢ cients of absolute and relative risk aversion. [8]
(c) Suppose that the agent has A = 1 to invest in two Önancial assets, one riskless and one risky. The price of the riskless asset is 1 and its return is 2, and short-selling on this asset is allowed. The price of the risky asset is 1 and its return is T with probability
distribution:
r = 1 with probability p1
r = 2 with probability p2
r = 3 with probability p3
Short-selling the risky asset is not allowed. If the agent invests a in the risky asset and 1 - a in the riskless asset, Önd the support of the probability distribution π = (π1 ; π 2 ; π 3 ) of the agentís portfolio return rP : If the agent maximises a von Neumann- Morgestern utility function u(W) of Önal wealth W , show that the optimal choice of a is positive if and only if the expectation of r is greater than 2 [Hint: Önd the Örst derivative of u(:) and calculate its value when a = 0] [8]
(d) Finally, Önd a when u(W) = 1 - exp(-bW); b > 0 and when u(W) = ( 
) W1-y ; 0 < y < 1 for the case in which π 3 >
π 1 : [6]
Section B
B1 The Equity Premium Puzzle and the Stock Market Participation Puzzle. [40]
(a) Explain as best you can what the Equity Premium Puzzle is. [13]
(b) Explain as best you can what the Stock Market Participation Puzzle is. [13]
(c) Are both Puzzles connected? Why or why not? [14]
B2 Testing the Capital Asset Pricing Model (CAPM). [40]
(a) Consider the following linear relationship between the return to an asset j , rj ; and the return to the market portfolio m, rm :
ajm
a m(2)
where rf denotes the return to the risk free asset, ajm denotes the covariance between the returns to asset j and the market portfolio m, and am(2) denotes the variance of the market portfolio return. Provide an interpretation of the above linear relation- ship. In particular, what is the risk premium of asset j? Why? What is the Beta of asset j? What is its relationship to non- diversiÖable market risk? Support your answers with the help of a graph, where you clearly identify the Capital Market Line and the E¢ ciency Frontier.
(b) Make all necessary assumptions to derive the CAPM principal estimating equation:
rj - rf = aj + gj (rm - rf ) + ∈j
where ∈j is i.i.d. N(0; 7
): In particular, show that gj = 
: [10]
(c) Suppose that you estimated the above relationship by OLS, and that you Önd that your coe¢ cient estimate of aj is signiÖcant and statistically di§erent from zero. Would this invalidate the CAPM predictions? Under which assumption(s) would you ex- pect the constant coe¢ cient estimate to be positive? Why? [10]
(d) Finally, describe a statistical procedure that would allow you to test the validity of the CAPM. (Hint: consider the Arbitrage Pricing Model. Does it nest the CAPM? Under which null hy-pothesis?) [10]
2023-01-17