## Khan Academy: "Finance: Basic Introduction to Risk and Reward"

Watch this video, which gives an example of the relationship between risk and reward.

The expected value is simply an average but with probabilities attached. For example, suppose that you have these three possible investment outcomes with their respective probabilities of occurring:

 Investment Outcome Probability Profit $100,000 0.30 Profit$50,000 0.40 No profit and no loss 0.30

Notice that the sum of these probabilities needs to add up to 1.00 (or 100%).  To compute your "average" profits, you need to consider their probabilities. This average is normally called the "expected value" in statistics. Using this example, the expected value is computed as follows: (100,000x0.30) + (50,000x0.40) + (0x0.30) = 30,000 + 20,000 + 0 = 50,000.  Therefore, you expect to receive \$50,000 from this investment project.  In general, the expected value formula is:

Expected Value = (outcome A x probability of A) + (outcome B x probability of B) + ... + (outcome of Z x probability of Z)

where the sum of the probabilities add up to 1.00.

The standard deviation does not have an intuitive meaning, but it is a measure of risk in finance.  When you are facing an investment project with several possible outcomes and you know their respective probabilities, you can compute the expected value of an investment project.  But when you also need to know the level of risk, you can compute the standard deviation as follows:

Standard Deviation = square root of

(outcome A - expected value)2  x  probability of A

+ (outcome B - expected value)2  x probability of B

+ ...

+ (outcome Z - expected value)2  x probability of Z

where the sum of the probabilities add up to 1.00.

In finance, an investor will take on more risk only if the return is higher, or vice versa.  This is what we call in finance the "risk-return tradeoff."