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How to calculate odds/expected return?

OK, this is non-technical and maybe not the best place to post, anyway.

I go hypothetical:

Let's say you have $10,000 to invest. There is an opportunity that within one year you can get back $13,000, but there is a chance that you will loose the invested money. They also say that you got 60% chance that you will get the $13,000 and 40% that you will loose it.

My question how people determine if this is a good bet or not? What calculation would you do and how? Also, are there any averages in industries or in investment companies which tells them that this is a good, average or a bad chance?

Do you have sources where can I learn this type of stuff?

Wednesday, February 25, 2004

I believe what you are looking for is a "risk premium" .  I'm not sure I can define it properly. but it basically is a way of calculating what your return should be for a given level of risk.  It's based on the "risk-free" rate of return, which is usually tied to yields on some form of US bond or treasury.  I believe (risk-premium = rate-of-return - risk-free-rate).

Hope this helps.

Wednesday, February 25, 2004

If I remember statistics (which I probably don't) I'd say that's a bad investment.  The expected return is:

$0 x 0.4 + $13,000 x 0.6 = $7,800

In my book investing $10,000 and having an expected return of $7,800 is a bad investment.  Have you considered the lottery?

(or maybe I just did the math wrong).

Either way, Junk bonds were a thing of the '80s.  Try reading a book about investments.  Joel recommends a few.  I'll recommend Personal Finance for Dummies by Eric Tyson.

Wednesday, February 25, 2004

Your expected return would be 0.6 * 13000 = 7800, while a U.S. bond would be 1.0 * 10250 = 10250. So you're better off buying the bond, or even betting it all on red in Vegas (0.474 * 20000 = 9474).

Statistics 101
Wednesday, February 25, 2004

A standard way to look at this type of situation is to walk the decision tree.

If I invest there is a 60% chance I make $3,000 and a 40% chance that I lose $10,000.

This is a pretty simple one, one decision node - multiply and add.... .6 * 3,000 + .4 * -10,000 = -2,200.  That's your expected return.  If you had a million instances to perform this operation, and walked each node an equal number of times, that's the average result you'd achieve.

Multiple decisions make the situation more complex, but it's all the same.  Build the tree and multiply across.

For slightly different scenarios there are different ways to determine if it is a good opportunity.

If this is something you're serious about I suggest picking up a textbook on decision analysis.  It's not a very complex topic, there's just a lot of options and decisions to be made during the analysis.

Wednesday, February 25, 2004

In gambler's terms your Expected Value (EV) on your $10,000 "wager" is $7,800. Or a negative EV of $2,200.

This is obviously a horrible bet.

Clutch Cargo
Wednesday, February 25, 2004

Horrible bet? Depends on the circumstances.

What if you need $13,000 for a life saving operation?

S. Tanna
Wednesday, February 25, 2004

>>What if you need $13,000 for a life saving operation?

Take out a bank loan for $3000, or borrow from a relative.  You need a pretty extreme set of hypotheticals before the proposed "investment" becomes attractive.

Wednesday, February 25, 2004

If I needed money for an operation I'm *not* going to go down to Dodgy Dave the Bookmaker and place money at those odds. 

a cynic writes...
Wednesday, February 25, 2004

Nice overview of investment theory.

Remember, if it sounds too good to be true (30% returns) it probably is.
Wednesday, February 25, 2004

"Remember, if it sounds too good to be true (30% returns) it probably is."

Berkshire Hathaway is up about 25% since August. That's a perfectly legitimate investment that will probably top 30% for the year.

Andy in Austin
Wednesday, February 25, 2004

And if you asked Mr. B what his expected increase on the investments was, he'd probably say "3%" or possibly, "0%".  He's a pretty shrewd man who makes smart decisions. Specifically he tries to avoid making bad decisions, and he admits when he does.  I believe his investor report from a year or two ago said something to the effect of, "So I sold the MacDonald's stock in favor of Disney stock.  It turns out that MacDonald's went up 10% while Disney stock took a tumble.  So you'd have been better off if I had used your money to go to the movies every day."

That said, investments don't exactly tie in to decision analysis of this sort.  There are many more possibilities and many more inputs than just a "Do I invest or not" scenario.

Decision analysis might be quite helpful for anyone monitoring a process or trying to determine what variables have the most siginicant effect on their output.  It might be that you're wasting all your time trying to make your server have a more reliable uptime when the time would be better spent fixing a "relatively small" bug in the data storage module because the latter has a larger influence on the outcome.  (You'd likely perform a Tornado analysis for that one).

If you're involved in a business area that can generate data and is responsible for generating decisions regarding business direction, influences, projects, or paths decision analysis might be quite beneficial.

Wednesday, February 25, 2004

> Do you have sources where can I learn this type of stuff?

MoneyCentral has lots of information for beginning investors.

as does

Eric Lippert
Wednesday, February 25, 2004

"Berkshire Hathaway is up about 25% since August. That's a perfectly legitimate investment that will probably top 30% for the year."

Damned Warren Buffet, skewing the averages.

Now where did I put that $100,000 of disposable income. (Okay I don't need to invest in THAT stock, I can get the $3,000 one.)

A quick look on Yahoo shows that the Nasdaq is outperforming it over the course of the past year anyway.

Now here's a question. Why does everyone get so emotionally involved in money matters? We spout trueisms and try to prove other people wrong to defend our own position. It happens any time money comes up on this board.
Wednesday, February 25, 2004

Unless it's at a casino, odds have nothing to do with this. Either the stock goes up or it goes down. No one can say that there's a 30% chance or a 75% or a 99% chance.

Whoever's estimating the odds is either lying to themselves or lying to you.

Wednesday, February 25, 2004

Thanks for all the answers. I'm not going to invest in stock (at least not now) but more interested in the general theory and areas where I can use that,

Eg. to calculate that you have a call center with 10000 phone calls a day, and you deal with 5 basic problems, each has it's own percentage. Now an automated system can track if it's worth spending 15 minutes with one customer, or after 5 you need to put the phone off as if you spend the other 10 with a better problem your average customer satisfaction will be better. In this case you invest time, and return value will be customer satisfaction (eg. more sales)

Wednesday, February 25, 2004

There are many situations where you need to put percentages on stock price movements.  M&A arbitrage is a big one (just to pick one example).  Investors would buy a stock at the announcement of a potential merger with the hope of making the spread.  One of the key variables here is the perceived odds that the deal will close. 

In this case the odds are obviously subjective, but most of the variables that could result in deal failure are known, so experienced players can make educated guesses at the odds.  These estimates are of course a source of risk, but the use of probablility is inavoidable.

Wednesday, February 25, 2004

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