QUESTION: Difference between Risk Neutral and Risk Averse with example MY ANSWER

Question

QUESTION:    Difference between Risk Neutral and Risk Averse with example

MY ANSWER

Difference between an investor who is risk neutral and one who is risk averse:

Risk-neutral: Risk neutral is indifference to risk. The risk-neutral investor would be in the middle of the continuum represented by risk-seeking investors at one end, and risk-averse investors at the other extreme. So what is a risk-neutral investor? As you might have guessed, a risk-neutral investor will make his or her decision mathematically. Say the payment were less than $50. If you are risk-neutral, you will choose the coin toss. If the payment is more than $50, you will choose the guaranteed payment. What if the guaranteed payment is exactly $50? According to economic definitions, a truly risk-neutral person would choose the guaranteed payment.

Risk-averse: If you are a risk-averse investor, you will find yourself immediately leaning toward the guaranteed payment. Depending on just how risk-averse you are, you may immediately accept it without concerning yourself with the amount. After all, some money sure beats no money. You do not perceive this as a “nothing to lose” scenario, because the guaranteed payment is technically yours by right should you accept it. You stand to lose that account receivable if you choose Option 2. But you might consider accepting the coin toss depending on the amount of the guaranteed payment of Option 1. Someone who accepts a guaranteed payment of, say, $20, is more risk-averse than someone who will only accept the guaranteed payment if it is $45, and might otherwise choose the coin toss and risk losing.

CONTRIBUTION FROM ONE OF MY CLASSMATES

RE: Difference between Risk Neutral and Risk Averse

I am a little confused on your risk neutral example. Here is how I interpreted it: The example mentions a coin toss and that the risk neutral person would pick the guaranteed payment over the unguaranteed payment if both options were worth the same amount of money. My conclusion below assumes that the coin toss is worth $100 and the probability of getting tails (winning side) is 50%, making the value of the coin toss $50. This would make both options worth $50 in the risk neutral person’s perspective.

(Coin Toss = $100*.5 Guaranteed = $50*1) In my opinion, I think that the risk neutral person would be just as happy to choose option one versus option two. According to an article I read, a risk neutral person is only concerned with the expected magnitude of gains or losses multiplied by the expected probability of realizing the gains or losses. If the guaranteed payment was chosen over the coin toss, assuming they are both worth $50, that would make a person risk averse. Thoughts?

https://cyber.law.harvard.edu/bridge/LawEconomics/risk.htm

PLEASE ADVICE ME BASED ON THE CONCLCLION

Explanation / Answer

The Risk-Averse Investor:

Yes, this is true that a risk-averse investor would generally choose the guaranteed payment. He believes that something is better than nothing. It is also true that the degree of risk-aversion is different for the different investors. Suppose a coin tossed and a head means a win of $ 100 and a tail means a lose and $ 0 payment and the coin in unbiased so expected payoff = 0.5* 100 +0.5 *0 = $ 50

In theory the guaranteed money of $ 50 and the above payoff of $ 50 are equal for any risk neutral person but that is not the case with risk averse. He can prefer any guaranteed money below $ 50, even $ 1 over the expected payoff of the toss of the coin. OR we can say that all the investors are risk averse who prefer guaranteed income from $ 1 to $ 49 over expected payoff of $ 50.

The Risk-Neutral Investor will be neutral or indifferent between both the choices; the guaranteed income of $ 50 and expected payoff of $ 50. Otherwise we will go for coin toss if guaranteed income is less than $ 50 or he will chose guaranteed income if it is more than $ 50. So in this case, he is neutral or indifferent at only one point that is $ 50.

The risk-seeking investor would take his chances with the toss of coin unless he is offered a guaranteed payout of more than $50. He may chose any income between more than $ 50 – to less than $ 100 as guaranteed income to give up expected payoff of toss of coin and it depends on his degree of risk seeking.

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