What risky share is optimal given return and risk aversion?
The risky share rises with excess return, falls with risk aversion and variance, and is clipped to feasible bounds.
Follow the cause and effect
Compute μ−rf in consistent units.
Divide by γσ² for the unconstrained share.
Use max-min clipping to enforce feasible holdings.
The model you are using
Conditions for this model
No short selling or leverage, so 0≤a≤1. Mean–variance is stipulated, not claimed sufficient for all return distributions.
The exam trap
Do not substitute standard deviation for variance in the denominator or ignore short-sale limits.
Connect the reasoning to the graph
What changes
- The objective in a is concave; its vertex may lie outside [0,1].
What stays fixed
No short selling or leverage, so 0≤a≤1. Mean–variance is stipulated, not claimed sufficient for all return distributions.
Keep these conditions throughout the comparison; change only what the case above specifies.
What to inspect
Use max-min clipping to enforce feasible holdings.
Compare before and after, and locate the conclusion on the graph.
5 MINUTES · TRANSFER THE IDEA
Can you explain it without the lesson?
Explain why doubling γ halves the risky share when no boundary binds.