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Suppose you are an associate at a prestigious investment firm. One day, your boss gives you the following exercise to test your basic quantitive skill you learned from FINM7008. Your investment opportunities are limited to five assets (1) ASX All Ordinaries Index; (2) Heng Seng Index; (3) Nikkei 225 Index; (4) S&P 500 Index; (5) CSI 300 Index. (See the Description sheet for details of these assets). He gives you the time series of 5 asset class monthly adjusted prices between 12/2008 and 12/2016 and assume a risk aversion coefficient of 3. Please report all answers in monthly terms.
(a). Find the minimum variance portfolio among these assets, and also report the resulting portfolio expected return, standard deviation and sharpe ratio.
(b). Do (a) again, but this time you are not allowed to short assets. How the results (e.g. expected return and sharpe ratio) change?
(c). Find the optimal allocation among these assets, and also report the resulting optimal complete portfolio expected return, standard deviation and sharpe ratio.
(d). Do (c) again, but this time you are not allowed to short assets. How the results (e.g. expected return and sharpe ratio) change?
(e). Do (c) again, besides no short sell, this time your boss gives one more restriction, the maximum weight of single type of asset can not exceed 30% (similar restriction as in mutual funds). How the results change?