Since we don’t know future returns, we will treat them as random
Our best guess for the future return is the expected value:
The amount of uncertainty in potential returns can be measured by the
variance or standard deviation.
What are \(\mu\) and \(\sigma\)?
It will often be convenient to assume asset returns are normally
As an example, suppose that
What do their probability distributions look like?
The assumption of normality is convenient because
Typically we don’t know the true mean and standard deviation of Amazon
and Coca-Cola. What do we do?
We don’t include dividends in the return calculation above, because we
use ADJUSTED closing prices, which account for dividend payments
directly in the prices.
Compute the sample mean of returns
Compute the sample standard deviation of returns
The “hats” indicate that we have estimated \(\mu\) and
\(\sigma\): these are not the true, unknown values.
Let’s collect the \(N = 13\) closing prices for Amazon and
Coca-Cola between 3 Jan 2012 and 2 Jan 2013.
We will typically assume that a risk-free asset is available for
The return on a short-term government t-bill is usually considered
If you can invest in a risk-free asset, why would you purchase a
risky asset instead?
The amount by which the expected return of some risky asset \(A\)
exceeds the risk-free return is known as the risk premium:
The excess return measures the difference between a previously
observed holding period return of \(A\) and the risk-free:
The Sharpe Ratio is a measure of how much risk premium investors
require, per unit of risk:
Suppose the monthly risk-free rate is 0.2%. What is the estimated
risk premium and Sharpe Ratio for Amazon stock?