Week 5 - Risk, return & the cost of capital Flashcards
Expected return formula
summationN pi Ri
Variance of returns formula (probability definition)
Sample variance (statistics definition, use if from PAST DATA/sample)
*standard deviation = VOLATILITY
- summationN pi [Ri - E(R)]
- 1/(N-1) summationN (Ri - Rbar)^2
Covariance & sample covariance formulas
Correlation & sample correlation formulas
The lower the correlation, the lower the __?
Lower correlation, lower risk
(but most assets, esp. stocks, have a positive correlation)
Variance of a portfolio: N asset case
How many terms will there be?
N assets -> N^2 terms:
N variances
N(N-1) covariances
N(N-1) / 2 individual covariance terms
Diversification
Portfolio variance formula
Diversified portfolio of stocks = a portfolio containing many stocks each w/ a fairly small weight
> portfolio risk decreases
As N becomes large…
- (left) AVG VARIANCE term tends to 0, so can DIVERSIFY AWAY the FIRM SPECIFIC RISK
- the whole right term tends towards the AVG COVARIANCE. However, cannot diversify away the SYSTEMATIC RISK. There are ECONOMY wide risk factors that generally result in a positive correlation/covariance between stock returns.
> The risk of a well-diversified portfolio depends on the market risk of the securities included in the portfolio
Beta (of asset i)
Portfolio beta
Covariance of the returns from the particular asset w/ the portfolio DIVIDED by variance of the returns of overall portfolio
- higher beta, more risk from stock i
{how much risk asset i contributes to portfolio p}
Portfolio beta, βp = summationN wi βi
How to interpret a stock’s beta of 0.4 to the market? How about beta of -0.25?
+ve beta = stock tends to move in the SAME direction of the market
- For every 1% rise (fall) in the market, expect stock to rise (fall) by 0.4%
-ve beta = stock tends to move in the OPPOSITE direction of the market
- For every 1% rise (fall) in the market, expect stock to fall (rise) by 0.25%
