Chapter 8 Lecture Notes - 8-07 - Chapter 8 The covariances...

Chapter 8
The covariances between securities are usually positive, because the same
macroeconomic factors affect all firms. Unexpected changes in these factors affect the
entire market.
We can sum all these macro factors into one indicator and assume everything else that
moves stocks is firm-specific and thus diversifiable.
r
i
= E(r
i
) + m
i
+ e
i
m
i
= impact of unanticipated macro events
e
i
= impact of unanticipated firm-specific events
E(m
i
) = 0
E(e
i
) = 0
Different firms have different sensitivities to these macro events.
F = level of unanticipated macro factor
β
i
= sensitivity of firm i to that factor
m
i
= β
i
F
Single Factor Model – Only one macro factor
r
i
= E(r
i
) + β
i
F + e
i
-- the single factor model
Use return on S&P 500 as a proxy for this one factor and we can call it the single-index
model because it uses the market index to proxy for the common factor.
In single-factor models, the excess return is the sum of 3 components:
r
i
– r
f
= α
i
+ β
i
(r
m
– r
f
) + e
i
α
i
= expected excess return if the market is neutral
β
i
= responsiveness to the factor
(r
m
– r
f
) = market movements. This is the one factor.
Why use excess returns?
If T-bill rate is 1%  8% is a result of good economic news
If T-bill rate is 10%  8% is a result of bad economic news

A convenience of the index model is that it says that the covariance between two stocks is