Portfolio:

All types of assets that people diversify. So, the important issue in portfolio is the portion of each type of asset. How to choose (or allocate) the combination of riskiness and rate of return will depend upon each person’s attitude toward riskiness or uncertainty.

Portfolio Selection Model:

Two types of assets: safe vs. risky assets

r_f : rate of return of safe (or risk-free) asset
r_k : rate of return of risky asset.

We can simply imagine that r_f < r_k .

To express the level of riskiness we are able to adopt the standard deviation of the rate of return (σ).

Therefore let’s assume that r_k has the standard deviation of σ_k .

Suppose a person has $1 worth of wealth and s/he wants to have a as a type of risky asset and (1− a) as safe asset. Based on this information we can calculate the rate of return of this portfolio (r_p) and level of riskiness (σ_p) as follows:

r_p = ar_k + (1− a)r_f  ........(ii)

σ_p = aσ_k      ...............(iii)

Finally, the question is to get the specific value of a in this portfolio selection model. Using utility function with the insertion of two factors, r_p and σ_p , we can set up:

U = U(r_p , σ_p)  .........(iv)

If this person is risk averse, s/he thinks that σ p will be a “bad.”

From (ii) we are able to get:

r_p = r_f + a(r_k − r_f)  ..........(v)

Plugging a = σ_p /σ_k into (v), we can get the final expression:

A: a = 0. B: a = 1

(rk −rf )/σk: price of risk

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