Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rate of Return and Risk

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Abstract
This paper examines changes in the optimal proportions of investment capital placed in a safe asset and in a risky asset by an expected utility maximizing risk averse investor. If the return for the safe asset increases and the risky asset distribution remains fixed, the optimal proportion invested in the safe asset will increase provided that the investor's absolute risk aversion is nondecreasing or his proportional risk aversion never exceeds unity. Otherwise, it can be optimal to decrease holdings in the safe asset when its return increases. If the return for the safe asset remains fixed and the risky distribution improves by a first degree stochastic dominance change, the optimal proportion invested in the risky asset will increase (or not decrease) provided that proportional risk aversion never exceeds one plus the product of the gross return for the safe asset times absolute risk aversion. Otherwise, it may be optimal to decrease holdings in the risky asset when its distribution improves in the indicated manner.

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