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Consider a two-period world (i.e., t = 0, 1, and 2) where risky-(Answered)

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Consider a two-period world (i.e., t = 0, 1, and 2) where risky asset returns are not IID. We

 

also assume that investors can balance portfolios during the interim period. A Markowitz

 

investor relies on the static portfolio choice theory we discussed in the first week of the

 

class, and a long-horizon investor relies on the dynamic portfolio choice theory we discuss in

 

the second week of the class. Both investors have the same risk aversion parameter value,

 

and has the same utility function. Evaluate the following statements about static and

 

dynamic portfolio choices, True or False? Explain briefly if the statement is False.

 

a) One of the fundamental differences between the Markowitz investor and the longhorizon

 

investor is that the Markowitz investor can carry out optimization period by period, while

 

the long-horizon investor can only carry out optimization at the beginning of the period (i.e.,

 

t = 0).

 

b) For a Markowitz investor in a two-period world, a two-period risk-free bond is a risky

 

asset; and for a long-horizon investor in a two-period world, a two-period risk-free bond is a

 

risk-free asset.

 

c) Let ? 1 and ?2 denote the utility associated with the Markowitz investor?s portfolio in the

 

first and second period, and ? = ?1 +?2. Similarly, let ? 1 and ?2 denote the utility

 

associated with the long-horizon investor?s portfolio in the first and second period, and ? =

 

?1 +?2. Then we always have ? > ?, ?1 > ?1, and ?2 > ?2.

 

d) For both the long-horizon investor and the Markowitz investor, they face the same

 

optimization problem at ? = 1; and they all solve a one-period Markowitz problem.

 

e) Let ?? ? denote the optimal weight in stock in the Markowitz investor?s portfolio at t =

 

0. Similarly, let ?? ? denote the optimal weight in stock in the long-horizon investor?s

 

portfolio. If stock return exhibits mean-reversion, while stock return volatility stays constant

 

over time, then ?? ? < ?? ?.

 

f) Let ?? ? denote the optimal weight in stock in the Markowitz investor?s portfolio at t = 0.

 

Similarly, let ?? ? denote the optimal weight in stock in the long-horizon investor?s

 

portfolio. If stock return between t=0 and t-1, ?1, is negatively correlated with return

 

volatility during the next period, ??2 2while expected stock returns are the same during

 

these two period, or ? (?1) = ?(?2) = ?, then ?? ? < ?? ?.

 


 

 

Paper#9209890 | Written in 27-Jul-2016

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