Risk and return will be very central terms in our analysis and it is essential that the reader clearly understands the meaning of each term and how assets with different payout structures can be compared. General utility theory suggests that the average investor is risk averse. Given the same expected return of two assets with different risks, he would prefer the one with less risk. (This assumption may not be perfectly true for all individuals in all situations, but for the investor community as a whole it is probably true). For an asset with uncertain cash flows and payoffs, which are normally distributed, the mean of the distribution will be the expected return while the standard deviation forms some kind of “risk”. Choosing the “less risky” asset therefore comes down to choosing the asset with the lowest standard deviation in its payout distribution. An investor could also approach the problem from the other direction, choosing among assets with the same risk and then choose the asset with the highest expected return. Risk is usually defined as the volatility of returns, measured by standard deviation. The variance of a portfolio depends not only on the individual variances of the as- sets, but also on the co-variances between the components of the portfolio. As an extreme example, a portfolio consisting of two securities – a long position in a stock and with an appropriately chosen position in a put option on the same stock – will have lower risk than either of its components because the two securities are negatively correlated. For practitioners, the main drawbacks to the focus on volatility is that it ignores other moments of the distribution of returns and treats both “upside” and “downside” risk symmetrically. For this reason, practitioners typically begin with volatility but also look at other risk metrics as well.

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