Find out expected return on the index and slandered devotion

Question

Find out expected return at last asset when return on the index and slandered devotion is given?

Answer 1

Let us show the expected return on the index with µM and its standard deviation with σM. The expected return upon the ith asset is then

µi = αi + βiµM

and the standard deviation

σ_i = √(β²_iσ²_M + e²_i)

The return is given as follows, if we have a portfolio of such assets,

We have

µ_Π = α_Π + β_ΠE[R_M] = α_Π + β_Πµ_M.

Likewise the risk in Π is measured with

Note that when the weights are all about similar, N-1, then the last terms inside the square root are also O(N-1). Therefore, this expression is, here to leading order as N →∞,