# Loss Aversion

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Hi guys,

I'm studying for the CFA Level 3 exam again and am thinKing about loss aversion and framing biases.

An investor is prompted with a scenario with where he can choose a 1 in 4 chance of receiving \$400 or \$75 guaranteed.

Now I know the math. I know that the first has a higher expected value and that generally its considered an irrational bias to choose the \$75 as many participants do. My question is on your opinions.  In certain circumstances, like this one, it seems that the irrational choice is my preference despite being aware of the "bias". My reasoning is below:

1) this is a one time event and there's no guarantee I'll play continuously

2) in a one time event scenario, there's a 75% chance of me losing with a 25% chance of winning big OR a 100% of me winning a little.

So I have two questions for you:

1) which scenario would you choose and why?

2) in your selected scenario, what would the alternative reward have to be to make you switch your choice (cetiris paribus)

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Easy, I go for the 25% chance for \$400. It's totally irrelevant that this specific event is a one time deal, because you should have a huge amount of other decisions that you can make during a lifetime. Maximizing the EV of all your decisions will in the long run generate a far superior outcome than always going for the low variance, low EV option. The only reason to go for a low risk/low EV option is when the amount at risk is very substantial. If you would ask this question to someone in Malawi who's surviving on \$10/month it's probably wise to go for the low EV option....

PS. I would only switch to scenario 2 if I would get paid \$100 or more.

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To figure this out you need to construct a personal utility function. I think it is quite rational to prefer a bird in hand versus two in the bush, as long as you have a consistent, well defined function that reflects your marginal utility and risk aversion.

I would take a 25% chance at \$400 over a guaranteed \$75. But I would take a guaranteed \$75,000 over a 25% chance at \$400,000. Utility functions are convex, so the marginal value of the 75,001 dollar is significantly less than the 1st dollar.

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let's say the number is larger and you have some other opportunities that are very juicy, but no money to act on it. That might not be available later. Then the guaranteed money right now could be better.

Except for that, I agree with Hielko

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There was a big debate about the Kelly formula regarding wealth optimization VS hapiness optimization. Basically most people's unhapiness will be so bad if they lost 75\$ that they will prefer the safe route. I suggest you read Fortune's Formula and Thinking Fast and Slow, they pretty much cover the whole subject.

For me I would be ready to take favorable bets any seconds of my life if it represents less than 5% of my net worth.

BeerBaron

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add 6 zeros to the end of your numbers, make it a one-time game, and the majority of people's answers will change. as constructive said, you need the utility curve to really answer it.

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add 6 zeros to the end of your numbers, make it a one-time game, and the majority of people's answers will change. as constructive said, you need the utility curve to really answer it.

I agree with this statement, but the material suggests that it shouldn't matter what the absolute level of the numbers is or continuous play. Basically the idea is you display a loss aversion bias that is "irrational" if you would play this game continously but not once. Same goes for if you'd play it for \$75,000,000 and not for \$75. This argument seems like BS to me though and the use of the utility function makes sense to me.I'm not going to much happier with 100M than I am with 75M but I'd certainly be super disappointed 3 out of 4 times walking away with nothing by taking the gamble with the "higher expected value". It definitely seems at some point that the "bird in the hand being worth two in the bush" is a very very reasonable and even rational approach.

I'm not trying to disprove the CFA material so much as I'm just trying to understand how most people think about this, what their decision would be, and what #'s would force them to change. More of out of curiosity than anything else.

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This is where Kelly's forumla comes into play.

Let's say you are playing head of tail. Head you win 3x the bet, tail you lose your bet. You have 10\$ seed money. How much should you play? If you bet all the time all your money you will end up one day or another with a total loss. If you bet 1% of your net worth you will be compounding very slowly. Kelly's formula tells you the sweet spot where you can't lose everything but where you'll compound your money the fastest.

BeerBaron

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add 6 zeros to the end of your numbers, make it a one-time game, and the majority of people's answers will change. as constructive said, you need the utility curve to really answer it.

I agree with this statement, but the material suggests that it shouldn't matter what the absolute level of the numbers is or continuous play. Basically the idea is you display a loss aversion bias that is "irrational" if you would play this game continously but not once. Same goes for if you'd play it for \$75,000,000 and not for \$75. This argument seems like BS to me though and the use of the utility function makes sense to me.I'm not going to much happier with 100M than I am with 75M but I'd certainly be super disappointed 3 out of 4 times walking away with nothing by taking the gamble with the "higher expected value". It definitely seems at some point that the "bird in the hand being worth two in the bush" is a very very reasonable and even rational approach.

I'm not trying to disprove the CFA material so much as I'm just trying to understand how most people think about this, what their decision would be, and what #'s would force them to change. More of out of curiosity than anything else.

There's not a "right " answer to this question. If you get a question like this on the exam, calculate the capital needed under the Kelly formula to support rolling the dice on the volatile option.  Then , explain that utility functions are typically nonlinear or situational.  for example, the gambler might be loaded and well able to risk losing the \$75, but he might want to impress the girlfriend on his arm by choosing the sure win, rather than looking like a fool by coming up empty handed when he could have had the sure thing.

that type of faulty (?) reasoning underlies most of the suboptimal herding of investment managers.

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This is where Kelly's forumla comes into play.

Let's say you are playing head of tail. Head you win 3x the bet, tail you lose your bet. You have 10\$ seed money. How much should you play? If you bet all the time all your money you will end up one day or another with a total loss. If you bet 1% of your net worth you will be compounding very slowly. Kelly's formula tells you the sweet spot where you can't lose everything but where you'll compound your money the fastest.

BeerBaron

You can be very limited if you only invest in common stock (not using options).  100% investment in a single common stock can lead to the total loss you mention.

Instead, using options, you can get at-the-money calls which represent a 100% notional upside position.  But then you pay for those calls by writing puts on 99 other companies.

You now have a portfolio of 100% concentrated upside in one name, but only 1% downside exposure in each of 100 different names.

These Kelly formula discussions never deal with these real world strategies.  It's all Ivory Tower stuff that leads to unrealistic fears about concentrated positioning.

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While utility functions are important, studies have shown that the average person is incredibly sensitive to loss aversion, even with coin flips for \$1 each for 20 rounds.

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This is where Kelly's forumla comes into play.

Let's say you are playing head of tail. Head you win 3x the bet, tail you lose your bet. You have 10\$ seed money. How much should you play? If you bet all the time all your money you will end up one day or another with a total loss. If you bet 1% of your net worth you will be compounding very slowly. Kelly's formula tells you the sweet spot where you can't lose everything but where you'll compound your money the fastest.

BeerBaron

You can be very limited if you only invest in common stock (not using options).  100% investment in a single common stock can lead to the total loss you mention.

Instead, using options, you can get at-the-money calls which represent a 100% notional upside position.  But then you pay for those calls by writing puts on 99 other companies.

You now have a portfolio of 100% concentrated upside in one name, but only 1% downside exposure in each of 100 different names.

These Kelly formula discussions never deal with these real world strategies.  It's all Ivory Tower stuff that leads to unrealistic fears about concentrated positioning.

Or, flip that around with this hypothetical.  Suppose one has a portfolio with stocks like Lancashire that pay high dividends and that the whole portfolio is loaded with what are -- I hate to use this term -- low beta stocks that are levered up with derivative, non recourse leverage that also levers up the amount of dividends received.

Further suppose that the intrinsic value of the portfolio is satisfactory even in an elevated market and that there is very little concern about a general market decline except for one thing : that it would be nice to have a big pile of cash to pick up bargains in the event of a market selloff.

In that event, taking a small portion of the dividends received and buying cheap index puts, might not be a bad strategy.

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add 6 zeros to the end of your numbers, make it a one-time game, and the majority of people's answers will change. as constructive said, you need the utility curve to really answer it.

I agree with this statement, but the material suggests that it shouldn't matter what the absolute level of the numbers is or continuous play.

Really? I'm pretty sure that the people at the CFA Institute know what an utility function is.

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This is where Kelly's forumla comes into play.

Let's say you are playing head of tail. Head you win 3x the bet, tail you lose your bet. You have 10\$ seed money. How much should you play? If you bet all the time all your money you will end up one day or another with a total loss. If you bet 1% of your net worth you will be compounding very slowly. Kelly's formula tells you the sweet spot where you can't lose everything but where you'll compound your money the fastest.

BeerBaron

You can be very limited if you only invest in common stock (not using options).  100% investment in a single common stock can lead to the total loss you mention.

Instead, using options, you can get at-the-money calls which represent a 100% notional upside position.  But then you pay for those calls by writing puts on 99 other companies.

You now have a portfolio of 100% concentrated upside in one name, but only 1% downside exposure in each of 100 different names.

These Kelly formula discussions never deal with these real world strategies.  It's all Ivory Tower stuff that leads to unrealistic fears about concentrated positioning.

I think this strategy looks quite appealing, but during market corrections, correlations among the 100 stocks tend to become close to 1, so the downside may not be truly diversified.

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I would like to revert the choices in real munger fashion  ;D

Either you lose 500 USD guaranteed or you chose to flip a coin and get away with 0 or lose 1000 USD. How would you react now with a potential loss instead of gain ? ::)

Same thing here, math suggests you should take the 500 USD loss but since we are dealing with human nature, most people would go for the 50% chance with the coin, this since many generally feel a loss twice as much than a profit.. meaning taking a higher risk to aviod a potential loss..

Lets then put this into practice in todays economic reality, in which I think is the important part.. Many are today faced with the ugly reality of either having their money in a bank account that pays nothing and go minus with inflation, or risk it on an asset class in the market - potentially losing twice as much. Since many go for the second choice the risk tolerence decline and risk aversion goes up making the market an even more dangerous place to be in..

So my answer to your question would be that instead of thinking of what your potential gain would be, first look at your downside risk before upside potentil.. Focus on minimizing risk..

Rgds,

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Further suppose that the intrinsic value of the portfolio is satisfactory even in an elevated market and that there is very little concern about a general market decline except for one thing : that it would be nice to have a big pile of cash to pick up bargains in the event of a market selloff.

In that event, taking a small portion of the dividends received and buying cheap index puts, might not be a bad strategy.

Similar to something else I think about, which is to buy out-of-the-money puts on individual companies that you both understand and want to own in the next crash.

Once their stock prices decline to the strike price of the puts, you have enough premium value in those puts to flip them into calls.  Then you profit on the recovery as the calls appreciate.

The benefit here is that the premiums for individual names might skyrocket -- this ensures you will be able to afford them without stressing out about the premiums.

Or in taxable portfolio margin account, just keep the puts and load up on the common (hedged by the puts).  This way there is no taxable event from selling the puts.

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This is where Kelly's forumla comes into play.

Let's say you are playing head of tail. Head you win 3x the bet, tail you lose your bet. You have 10\$ seed money. How much should you play? If you bet all the time all your money you will end up one day or another with a total loss. If you bet 1% of your net worth you will be compounding very slowly. Kelly's formula tells you the sweet spot where you can't lose everything but where you'll compound your money the fastest.

BeerBaron

You can be very limited if you only invest in common stock (not using options).  100% investment in a single common stock can lead to the total loss you mention.

Instead, using options, you can get at-the-money calls which represent a 100% notional upside position.  But then you pay for those calls by writing puts on 99 other companies.

You now have a portfolio of 100% concentrated upside in one name, but only 1% downside exposure in each of 100 different names.

These Kelly formula discussions never deal with these real world strategies.  It's all Ivory Tower stuff that leads to unrealistic fears about concentrated positioning.

I think this strategy looks quite appealing, but during market corrections, correlations among the 100 stocks tend to become close to 1, so the downside may not be truly diversified.

The point of diversification isn't to prevent the portfolio from declining in market corrections, it's to prevent you from single-company risk.

So you don't wind up being 100% concentrated in JPM when the next London Whale comes along on a scale of 20x the size of the last one.

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This is where Kelly's forumla comes into play.

Let's say you are playing head of tail. Head you win 3x the bet, tail you lose your bet. You have 10\$ seed money. How much should you play? If you bet all the time all your money you will end up one day or another with a total loss. If you bet 1% of your net worth you will be compounding very slowly. Kelly's formula tells you the sweet spot where you can't lose everything but where you'll compound your money the fastest.

BeerBaron

You can be very limited if you only invest in common stock (not using options).  100% investment in a single common stock can lead to the total loss you mention.

Instead, using options, you can get at-the-money calls which represent a 100% notional upside position.  But then you pay for those calls by writing puts on 99 other companies.

You now have a portfolio of 100% concentrated upside in one name, but only 1% downside exposure in each of 100 different names.

These Kelly formula discussions never deal with these real world strategies.  It's all Ivory Tower stuff that leads to unrealistic fears about concentrated positioning.

I think this strategy looks quite appealing, but during market corrections, correlations among the 100 stocks tend to become close to 1, so the downside may not be truly diversified.

The point of diversification isn't to prevent the portfolio from declining in market corrections, it's to prevent you from single-company risk.

So you don't wind up being 100% concentrated in JPM when the next London Whale comes along on a scale of 20x the size of the last one.

Yeah. That makes sense. I guess you can diversify away the sort of Black swan fraud risk that brought down Barings Bank. Maybe simpler to just write put on S&P index. More diversified than 100 names.

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Because they are used for swapping risk.

Loss averse people use them.

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Optionality is one if the best ways to deal with loss aversion.  For example, in our business our bank offered us as good a rate on a slice of a pool of tax free bonds as we were were getting on our regular cash balances.  They guaranteed in writing to buy them back on short notice at our purchase price anytime we wanted to go to cash.

That was extraordinary, basically a free put.  It made me question the wisdom of not only our mid sized bank , but the entire banking system in the mid 00's.

We got an effective after tax rate of about 2% higher than otherwise.  Then, we exercised our put in late 07 as we anticipated counterparty risk as the system appeared to be on the verge of becoming unglued then.

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Buffett appears to be quite the fan of options, actually.

BAC

GS

etc...

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Similar to something else I think about, which is to buy out-of-the-money puts on individual companies that you both understand and want to own in the next crash.

Once their stock prices decline to the strike price of the puts, you have enough premium value in those puts to flip them into calls.  Then you profit on the recovery as the calls appreciate.

The benefit here is that the premiums for individual names might skyrocket -- this ensures you will be able to afford them without stressing out about the premiums.

Or in taxable portfolio margin account, just keep the puts and load up on the common (hedged by the puts).  This way there is no taxable event from selling the puts.

Can you flesh this out in an example?

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Buffett appears to be quite the fan of options, actually.

BAC

GS

etc...

Yup. If one can protect the downside, ( margin of safety ) then goosing the upside often makes sense. :)

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What is a good introduction book to options for an idiot like me?

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