Proof of Risk Aversion....

[Capitalist]

I posted this from another list about 18 months ago, but it probably is worth repeating as things are a bit slow and some of the newer people may not have seen it. If you have I apologise ;)

<<The discussion on risk made me think of the following
inductive proof on risk aversion I learned a few years
back.

Imagine you are offered the following game: You will
flip a coin. If it's tails, the game is over, and you
get nothing. If it's heads, you win two dollars and
keep going. You flip again, and if it's tails, the
game's over and you leave with your $2. If it's
heads, you win $4 (total, not in addition to your
previous winnings) and keep going. Again, if it's
tails, you leave with your $4, and if it's heads you
win $8 and keep going. This continues until you
finally get a tail.

You cannot lose money from this game, only win it.
However, imagine that the person running it charges
you a set fee in order to play. How much would you be
willing to pay to play this. Quick, throw out a
number before reading farther.
*
*
*
*
*
*
*
*
*
*
*

...

To figure out how much you should pay, you should
figure out the expected value of the game. There's a
1/2 probability you'll get nothing. (If the first
toss is tails.) There's a 1/4 probability you'll get
exactly $2. (Heads then tails.) There's a 1/8
probability you'll get exactly $4.
(Heads-heads-tails) And so on. So the expected value
of playing the game is:

(1/2)*0 + (1/4)*2 + (1/8)*4 + (1/16)*8 + (1/32)*16 +
...

This equals:

0 + (2/4) + (4/8) + (8/16) + (16/32) + ...

Which of course equals:

0 + 1/2 + 1/2 + 1/2 + 1/2 + ...

Which doesn't converge. The expected value of the
game is infinite.

Head scratcher time. How many of you said they'd pay
an infinite amount of money to play this game? I
don't see too many hands raised. Which makes sense.
Would you really bet everything you own, leaving
yourself penniless on the street, to play a
game where there's a 50% chance you'll be left with
nothing? And where there's only a 1 in a thousand
chance you'll get more than a thousand dollars?

My suspicion is that very few people said they'd pay
more than $10 to play, and almost nobody offered more
than $100. Even now, that you've seen the math and
know the expected value is infinite, I doubt you'd pay
more than $100 to play.

People are risk averse, QED.>>

[zyreon]

I'm not risk averse....


I bought some RMGOB :D[:o)]

[Capitalist]

:D:D:D

I find behavioural finance interesting. I read this about our much maligned broker friends:

Full service brokers and advisors are often hired despite the likelihood that they will underperform the market. Researchers theorize that an explanation for this behavior is that they play the role of scapegoat. In Fortune and Folly: The Wealth and Power of Institutional Investing, William M. O'Barr and John M. Conley concluded that officers hired investment managers for no other reason than to provide someone else to take the blame and that the officers were motivated by culture, diffusion of responsibility, and blame deflection in forming and implementing their investment strategy.

"In summary, people trade for both cognitive and emotional reasons. They trade because they think they have information when they have nothing but noise, and they trade because trading can bring the joy of pride. Trading brings pride when decisions turn out well, but it brings regret when decisions do not turn out well. Investors try to avoid the pain of regret by avoiding the realization of losses, employing investment advisors as scapegoats."

[Gryffyn]

Maybe they can do math and they're risk aware!

Cute example. I like the stuff about full-service brokers. Human nature is a wonderful thing.

[zyreon]

broker/adviser 101

first topic:
How to write ambiguous legalistic letters which "explain" the decrease in value of the clients' investments.



so much for personal responsibility...

[Cooper]

Studying Kahneman and Tversky's research into exactly that for a second year Econ paper Cap, they found that people place more "value" on a loss than a gain even though the two were the same in numerical terms. This means that people are that risk averse that they will sometimes turn down a choice that would be clearly beneficial to them. Worth bearing in mind when looking at supposedly risky investments, the returns offered in order to entice an investor may be proportionately high relative to slightly less risky investments. Good Post.

[stormrose]

Cooper: You gotta balance that against the gambling instinct - where loss is forgotten and gains are celebrated and remembered. There's plenty on research on this one.

[Gryffyn]

Coop/Stormy - just listen to any regular TAB punter talking about there weekend. It's all about the wins and not much about the losses.

Frankest I ever heard was when chatting to a guy at a blackjack table at Sky City about a year after it had opened. He said he'd been coming there regularly for 6 months and when I asked him how he was doing he said he was down about $8000!

[Cooper]

You could argue that gamblers are buying a service and are therefore willing to pay to feed their "fix". Either they are willing to accept the money lost as the "fee" for playing.

[Cooper]

Obviously the guy who is betting at Sky City is in it for more than a money making enterprise... at least you'd hope so!

[Gryffyn]

You're right but it's interesting that although they are willing to take the risk and keep on doing it/losing, they strangely are embaressed to admit their losses.

Back to Caps post - it's timely as many comentators think NZers misjudge risk/return esp with debentures - perversly often picking the lower return as safer even tough they are actually not as secure.

Fool and money soon parted - fool is lucky to get the money in the first place.

[belgarion]

Nice little theorem Cap ... But seriously flawed.

If you can't see why, then Id suggest you stay well away from the sharemarket ... ;)

[thereslifeafter87]

That game example is flawed because it is dependent on how much you can afford to lose.

Looking at it conservatively, I wouldn't have been prepared to pay more than $4 to play. The odds just aren't worth it. There is only a 25% chance that I will recover my $4.

But if I just wanted to have a laugh, I could probably easily afford to lose $20 on such a gamble.

[TheBossMan]

same topic covered as problem-solving, decision-making and operations research. We routinely pay insurance when it is labelled as "premium", even though the probability of it being a 'loss' is relatively high;

Our decisions are not rational, but mostly bounded.

I recommend "decision traps" by Edward Russo.

[stormrose]

The game above is zero sum - but only if you can afford to lose an infinite amount before walking away.

Take a look at roulette ... bet only red or black and you're in a similar situation. Basically the house can afford to lose more money than you.

Then the house has the greens to give it a slight edge.

[Gryffyn]

And a ceiling on betting amount to stop the double or nothing approach.

[PGL]

Good Post Capitalist and food for thought

A good opportunity for those with money to invest and an infinite amount of time to wait for an expected large return.

NOG & NOGOC offer the same opportunity

Disc NOGOC

[Tinker]

Re risk adversion I recall several studies which, paraphrased, showed that people felt 2 1/2 times as much pain for a set loss as they did pleasure for the same gain. And on the assumption that most people wish to avoid pain and maximise pleasure ( not applicable to all on this site perhaps?)then one may invest to minimise losses and maximise gains based not on a random expectation (or even based solely on fundamentals or TA) but slanted by the above mentioned beahvioural outcome.
Certainly for me emotionally a 20% loss "hurts" more than a 20% gain makes me feel "good". This probably makes me irrationally risk adverse.

Anybody still awake:)?

Cheers

[Cooper]

And apparently people will pay more to maintain the status quo than they will to get it in the first place.... worth remembering when you're weighing the idea of selling a stock, as you may place more value on it than it's worth (and I know some experienced "Old Schoolers" out there are going to tell me they wouldn't do this because they're too rational and act simply on the figures blah blah blah...)

[craic]

People with serious heart conditions are cautioned to avoid racetracks - not because of their losses - a winner is far mopre likely to trigger a heart attack.

[skinny]

I've read a few pop articles on the behavioural finance literature (unfortunately Kahneman and Tversky's stuff came a bit late for my econ studies) and I can fully relate to the fear of losses side. Like most economists I know I'm fairly risk adverse, e.g. the student loan and mortgage were fully paid off before even touching the share market!

However, I know that risk and reward is positively correlated over long time periods and like everyone else on ST I'm rather interested in the later aspect [:p].

My *personal* solution to this awful dilemma is holding a portfolio of around 10 stocks wherein the largest holdings are companies with relatively stable dividend and profit streams that I have done a fair amount of DD on. This gives me the confidence to invest in some smaller cap and/or more speculative plays which I know should boost the portfolios longer run performance. More importantly the diversifiaction enables me to 'switch off' the pain when they go on a losing run!

[Cooper]

I do as you do skinny, but I use leveraging for the smaller caps/ speculative plays.