## November 29, 2005

### Expected value and value to be expected

I saw this concept in the book ‘A mathematician plays the stock market’ which I am reading currently and liked the explaination and its relevance to me as an investor.

Expected value is essentially the sum of product of gain/losses from an investment and the associated probabilities. The expected value is the most likely result from an investment.

Let me explain

Let us consider a stock S. I have reasons to believe that the stock would decrease in value by 10%, with a 80% probability. At the same time, there is a long shot product if successful could result in bumper profits and could increase the stock price by 100%. However the chances are just 20% for this event.

So in the above scenario the expected value from the stock is = (-10%)*.8+(+100%)*.2 = 12%
However value most likely result to be expected from such as stock (atleast 80% of the time) is a return of –10%.

A large group of positive ‘expected value’ investment with negative ‘value to be expected’ should be profitable over a period of time. This is same as the principle of arbitrage or value investing from ben graham. The above concept is also critical if one is dealing with options. For example, sellers of put options have a negative expected value (sometimes very high), but a small positive ‘value to be expected’.

So next time if some analyst talks of a positive ‘value to be expected’, you may want to check the assumptions and figure out the ‘expected value’ of the recommendation

abhi said...

Excellent blog. I read a similarly explained concept in the booke 'Fooled by Randomness' by Nasim Taleb. He is a option trader.

Rohit said...

yes, you are right. The same concept is explained very well in the book. Actually nasim taleb follows the expected value approach towards options - taking lots of small losses for a large but infrequent payoff (which would be emotionally tough)