INVESTMENT TOOLS - JENSENS MEASURMENT

JENSEN’S PERFORMANCE
MEASURE (ALPHA)
The Jensen measure called alpha, involves an ordinary
least-squares regression to calculate risk-premium for an asset’s return and the market return. A positive alpha means that the asset performed better than the market
(e.g., Standard & Poor’s 500) in risk-adjusted terms. A negative alpha means the
opposite. If alpha is zero there is equality of return between the asset and the market on a risk-adjusted basis.
How Is It Computed?
Jensen’s formula is (ri - rf) = a + b (rm - rf)
where
(ri - rf) equals risk premium for portfolio i or asset i.
rf equals risk-free rate.
rm equals market return.
b equals beta coefficient.
a equals Jensen’s performance measure (also termed alpha).
ri equals return on portfolio i or asset i.
The alpha is computed with the ordinary least-squares regression subject to a
sampling error. The alpha may or may not be statistically significant.
Jensen’s alpha may be used to rank the performance of a portfolio when it is
appropriately adjusted. The adjustment involves dividing each asset’s alpha by the
beta coefficient. For example, if assets X and Y are being ranked, use the ratio a/b.
Example: The ABC Fund, T-bills, and the Standard & Poor’s 500 had the following
returns over the previous five years.