Question

A young couple has $28,000 (90% of their savings) to invest in either savings bonds or a real estate deal. The (zero coupon) savings bonds return $35,000 ($7,000 interest) in three years. The (completely liquid) real estate investment, after three years, is worth $66,000 if economic conditions are good (70% chance), and worth nothing ($0) if economic conditions are bad (30%). The couple decides to invest in the savings bonds.

What do you know about the certainty equivalent (for the couple) of the real estate investment?   HINT – Make sure you understand the concept of certainty equivalence.

What would you do in these circumstances?

Give me an example of a different set of probabilities that would change your decision in b”.

Answer 1

Ceratinty equivalent is a guaranteed return accepted by a consumer rather than a higher but uncertain return.

In this case,

Option A - 100% assurance of getting $7000 profit

Net expected value = 7000

Option B - 70% chances of getting a profit ( 66000 - 28000) = 38000

30% chances of losing all money, i.e. 0 ( Loss of $28000)

Net expected value = 0.7x38000 - 0.3 x 28000 = 18200

However, the couple chooses the conservative approach of going for savings bond rather than a high return but risky proposition of real estate.

Choice of option depends on the risk apetite of an individual. I would have chosen the option B. However, the decision would have been different if the probabilities are, say 0.6 and 0.4 respectively, in which case the NEV will be

= 0.6x38000 - 0.4x28000 = 22800 - 11200 = 11600

Here, the premium of $4600 is not good enough to take a risk of losing your savings with a chance of 40%, and the option A is more appropriate. Hence it can be said that any risk above 35-40% is not advisable.