ECOS3021 1
Tutorial 6 Attempt all problems beforehand to engage in class discussion. No detailed written answers will
be made available on Blackboard. We will go through them in class. Tutorial exercise problems
N.B. The following questions cover the examinable material for the mid-semester test: questions
1, 2(a), 3, 4(a), 5(a) & 5(b). No written answer will be available before we go through them in
class.
1. Consider an asset with annual volatility (σ) of 40% with the market beta of 1.2. Suppose that
the annual volatility of the market is 25%. What percentage of the total volatility of the asset
is attributable to non-systemic risk?
2. Consider the following utility function
1−γ c
u (c ) =
, → u ′(c) = c
1− γ −γ (a) Show that the relative risk aversion coefficient is given by γ. How do you interpret this
coefficient?
The elasticity of intertemporal substitution in consumption (i.e. the willingness to shift
consumption across time) is defined as ε =− ∂ (c1 / c2 ) ( p1 / p2 )
∂ ln(c1 / c2 )
or −
â‹…
∂ ( p1 / p2 ) (c1 / c2 )
∂ ln( p1 / p2 ) Note that if you let the price of period 1 consumption be one unit the price of period 2
consumption is 1/(1+r), where r is the real interest rate in units of consumption.
(b) The intertemporal efficiency in consumption is given by the equation (also known as the
consumption Euler equation)
u' (c1) = β(1 + r) u' (c2)
Use the above utility function to show that the elasticity of intertemporal substitution ( ε )
is the reciprocal of the relative risk aversion parameter (γ). What does this mean? ECOS3021 2 3. Assume that the utility function is u(c) = lnc. Note that the marginal utility, MU (c), is given
by u ′(c) = 1/ c . Suppose that c1 = 1 but the outcome of c2 is contingent on the state (s) of the
economy, as follows.
Bad (s1)
Good (s2) c2 = 0.5
c2 = 1.5 Probability = 0.5
Probability = 0.5 (a) Calculate the implied rate of return for the one-period discount bond, with a guaranteed
payoff of 1 consumption unit in period 2. Assume that the time preference factor β =
0.95.
(b) Now, consider a stock with the payoff structure that gives you the above state contingent
consumption. That is, this asset is perfectly correlated with the economy and provides
total consumption stream in period 2 as shown above. Determine the price of this stock
and the expected return. 4. Consider a two-period economy with given incomes y1 and y2.
In equilibrium, c1 = y1 and c2 = y2. Suppose that life time expected utility is given by
(c1 , c2 )
U= 1 1−γ
1 1−γ
c1 + β
c2 ,
1− γ
1− γ where γ > 0. (a) Write the consumption Euler equation linking between c1 and c2.
(b) The consumption-CAPM (C-CAPM) defines the stochastic discount factor or pricing
kernel as
mt +1 = βu ′(ct +1 ) / u ′(ct )
from the asset pricing version of the Euler equation,
=
1 Et [(1 + r )mt +1 ] .
What is the economic interpretation of m? Find m using the above utility function.
(c) Consider the price of q1 of a riskless asset such as a non-state contingent bond, which
pays 1 in any state in period 2. Suppose that c1 and c2 can take on any two values, 1 and
2, each with probability 0.5 and that c1 and c2 are independently distributed. Suppose that
β = 1 and also assume that γ = 2. What is the variance of the interest rate on bond?
(d) Now suppose that γ = 4. Again find the variance of the interest rate. Is it larger than the
variance of the gross consumption rate (c2/c1)? ECOS3021 3 5. One challenge for the C-CAPM is to explain that equities (stocks) tend to have higher returns
than bonds. This question links each type of return to aggregate, real activity. Consider a
two-period economy with a representative consumer (investor) whose consumption Euler (i.e.
intertemporal efficiency) equation is: where ri is the return on any asset. Let β = 0.9. Suppose that c1 = 1 and let c2 =1.1 with
probability 0.5 and 0.9 with probability 0.5.

• 1498093059-Tute 62.pdf

SuperTutor

(15)

Status NEW Posted 22 Jun 2017 12:06 AM My Price 15.00

-----------

Attachments

file 1498093059-Solutions file.docx preview (56 words )

S-----------olu-----------tio-----------ns -----------fil-----------e -----------Hel-----------lo -----------Sir-----------/Ma-----------dam----------- T-----------han-----------k y-----------ou -----------for----------- yo-----------ur -----------int-----------ere-----------st -----------and----------- bu-----------yin-----------g m-----------y p-----------ost-----------ed -----------sol-----------uti-----------on.----------- Pl-----------eas-----------e p-----------ing----------- me----------- on----------- ch-----------at -----------I a-----------m o-----------nli-----------ne -----------or -----------inb-----------ox -----------me -----------a m-----------ess-----------age----------- I -----------wil-----------l b-----------e q-----------uic-----------kly----------- on-----------lin-----------e a-----------nd -----------giv-----------e y-----------ou -----------exa-----------ct -----------fil-----------e a-----------nd -----------the----------- sa-----------me -----------fil-----------e i-----------s a-----------lso----------- se-----------nt -----------to -----------you-----------r e-----------mai-----------l t-----------hat----------- is----------- re-----------gis-----------ter-----------ed -----------onÂ----------- th-----------is -----------web-----------sit-----------e. ----------- H-----------YPE-----------RLI-----------NK -----------&qu-----------ot;-----------htt-----------p:/-----------/wo-----------rkb-----------ank-----------247-----------.co-----------m/&-----------quo-----------t; -----------\t -----------&qu-----------ot;-----------_bl-----------ank-----------&qu-----------ot;----------- -----------Tha-----------nk -----------you----------- -----------

Not Rated(0)

• Buy Answer