Frequently Asked Questions in Quantitative Finance by Paul Wilmott

Author:Paul Wilmott
Language: eng
Format: mobi, pdf
Publisher: Wiley
Published: 2010-05-18T21:00:00+00:00

Example

Historically a stock has grown by an average of 20% per annum when the risk-free rate of interest was 5%. The volatility over this period was 30%. Therefore, for each unit of risk this stock returns on average an extra 0.5 return above the risk-free rate. This is the market price of risk.

Long Answer

In classical economic theory no rational person would invest in a risky asset unless they expect to beat the return from holding a risk-free asset. Typically risk is measured by standard deviation of returns, or volatility. The market price of risk for a stock is measured by the ratio of expected return in excess of the risk-free interest rate divided by standard deviation of returns. Interestingly, this quantity is not affected by leverage. If you borrow at the risk-free rate to invest in a risky asset both the expected return and the risk increase, such that the market price of risk is unchanged. This ratio, when suitably annualized, is also the Sharpe ratio.

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