Variance of Return
: Why are we interested in the variance? One measure of how "risky" an asset is . There are others -- Range, Mean Absolute Deviation, Value at Risk, and so on We prefer variance because it is tractable Given the variance of individual assets, we will get clean formulas for the variance of portfolios of those assets Not possible with other measures of risk
Calculating ER
One way to calculate E and V is to imagine all possible states tomorrow, decide what the probabilities of those states occurring are, and calculate as we did in the previous slides Hard, and subjective Another way is to use historical data directly
Calculating ER and Var R
Suppose we don't know the possible states for IBM (so we can't calculate the expected return) All we can do is observe the returns, every month, for a long time What return series will we observe? If the series is very long, how many 21s, 10s, and -1s will we observe? Suppose we take the average of our observations, what should we see? This conclusion: that the average is a good approximation of the expectation is called the "Law of Large Numbers" Necessary that there is a long sample (why?) Necessary that whatever has generated the returns in the past continues to generate the returns in the future I don't care about the past
Historical data
Apply this idea to historical returns Example: we download monthly data on IBM from 1 Jan 2011-1 Jan 2013 from Yahoo Finance We have 24 monthly returns Average returns look like expected returns, so calculate aver