# Convexity and Indifference Curve

Hello Experts,

My question is about the preference of an indifference curve for a risk-averse investor. The most risk-averse investor will have an indifference curve with :

a) greatest slope coefficient

B) Most Convexity

Why is B wrong? Official answer is A. For risk-averse investor, if greater risk should be compensated with greater returns, then convexity should be correct. Please see the image I have drawn.

http://tinypic.com/r/iqbpme/8

Suppose that investor A’s indifference curves are all, in fact, straight lines with a slope of 5 (= 5% additional return per 1% additional σ of returns). Suppose that Investor B’s curves all start (at the left) with a slope of 1 and curve up to a slope of 3 as σ increases (to the right).

Investor B’s indifference curves will be more convex than investor A’s, but investor A is more risk averse.

S2000magician,

Thank you for your response. Can you please explain, in your example, why Curve B is more convex than Curve A. I have drawn a figure, but I couldn’t understand your post. Can you please explain this a bit?

http://postimg.org/image/4wiebd6hv/

The picture you drew for investor B is a straight line. It should be a curve, with a slope of 1 at the left end and a slope of 3 at the right end; thus, it curves up to the right, and that’s the convexity.

I think I can take a shot at this that might be a little bit easier to understand. Technically, with CFA stuff, you have to choose the MOST correct answer, so think of it this way.

Since it isn’t mentioned in the question, remove the constraint of the CAL or CML in your analysis, and don’t assume that the two investors will be operating with indifference curves that are tangent to the same CAL. Now the picture becomes more clear. See the (very poorly drawn) example, where you don’t have the constraints of the CAL. Blue Investor is clearly more convex, but actually less risk averse (willing to accept lower returns at same std dev) than Red Investor. However, if you draw the tangential line at the two curves, the slope coefficient for Red Investor is greater, despite having less convexity. http://tinypic.com/r/2cxglj7/8

Hello S2000magician,

I have corrected the pic below for checking my understanding and for others who are reading this forum. Please let me know whether this is correct.

http://tinypic.com/r/t7il5d/8