There are n assets with random returns X 1 , ,X n The term return means that, if you invest $1 in, say, the first asset, you will get an income of X 1 dollars Note that a return may be less than one Assume that X 1 , ,X n are i i d , E X i m, Var X i 2 Consider two strategies of investing n units o...

Let Y and Y2 be the total returns for the first and second stra ...

There are n assets with random returns X 1 , ...,X n . The term return means

Question:

There are n assets with random returns X₁, ...,X_n. The term “return” means that, if you invest $1 in, say, the first asset, you will get an income of X₁ dollars. Note that a return may be less than one.

Assume that X₁, ...,X_n are i.i.d., E{X_i} = m, Var{X_i} = σ². Consider two strategies of investing n units of money: either investing the whole sum into one asset, for example, into the first, or distributing the investment sum equally between n assets. For both strategies, compute

(a) The expected total return, i.e., the return per unit of money; and

(b) The standard deviation of the return. Proceeding from what you got, compare the two strategies.

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