Portfolio Theory

Explain why idiosyncratic risk is an ‘unnecessary’ risk.

• Idiosyncratic risk is the risk unique to each stock and is not linked to the overall market.

• When you average returns across many stocks, these unique risks cancel each other out.

  • aka diversification

• With enough stocks, idiosyncratic risk drops to zero, and only common (market) risk remains.

• Since you can always invest in a group of stocks, idiosyncratic risk is avoidable and unnecessary!!

Explain why we shouldn’t expect unnecessary risk to be compensated.

• Investors want higher returns for taking on risk.

• You don’t get extra returns for idiosyncratic risk because you can easily get rid of it by owning many stocks.

• Since idiosyncratic risk can be avoided, investors don’t need extra return to compensate for it

Explain why we think a security with more factor risk should have a higher expected return. In doing so, what evidence can you state that supports this view? 

Finally, what is the expected return on a diversified investment in stocks?

• Factor (market) risk is built into all stocks — you can’t diversify it away.

• When you invest in many stocks, you’re still exposed to the average market risk (beta).

• Because you can’t avoid this risk, investors expect higher returns to make it worth it.

• The proof is the strong 7.5% average return above risk-free investments seen over history.

Name the three primary economic considerations that we think go into determining a discount rate.  I am not looking for specifics, I am just looking for big picture, conceptual considerations.

1. inflation

   1. protect against the loss of purchasing power over time

2. real return

   1. to reward the use of your money

3. risk premium

   1. to compensate the uncertainty or risk of the investment

Using the figure, explain which of the three considerations in your answer to question (2) has the most important impact on stock discount rates, and why.  

• inflation — over 100 years, prices increased about 8 times

• The real return adds about one more doubling.

• The risk premium adds about 512 times growth

• The risk premium is the biggest part of expected returns

  • expected returns are what set discount rates.

What is systematic risk? Explain why we should expect systematic risk to be compensated.

• systematic risk affects the entire market (recessions, interest rate changes)

• you CANT get rid of it through diversification

• Because you’re stuck with it, investors expect to earn higher returns to make taking that risk worth it.

When we diversify from 5, to 25, to 100 or more stocks, 

What happens to the variance of returns?  Does it go to zero?   Why or why not?

• The graph shows how adding more stocks to a portfolio reduces risk (variance in returns).

• variation drops fast with about 20 stocks, but it doesn’t go to zero.

• That’s because systematic risk (market risk) can’t be diversified away — it always remains.

Why do we care about variance and why is this formula our measure of variance?

• Variance is the average of all these squared differences

  • measures how much returns vary.

• We care about variance because returns affect our wealth, and we don’t like uncertainty in our wealth.

• in the parentheses shows the difference in actual return from what we expected.

• Sometimes it’s higher, sometimes lower

  • when we square it, it’s always positive.

Why do we care about standard deviation and why is this formula our measure of StDev

• Standard deviation fixes the problem with variance, which is measured in weird (squared) units.

• Standard deviation puts it back into normal return units, which makes more sense.

• We care about standard deviation because, like variance, it measures uncertainty in our wealth.

Why do we care about covariance and why is this formula our measure of covariance?

• Covariance shows how two investments move compared to their averages at the same time.

• If they move together covariance is positive.

• If they move opposite covariance is negative.

• Covariance is larger when both investments have bigger ups and downs (higher standard deviations).

• We care about covariance because, in a portfolio, it’s a main driver of overall risk — more important than the risk of any single investment.

Correlation is defined as covariance divided by the product of the standard deviations:

It turns out that, with this expression, correlation is always between -1 and +1.  

what is the difference between the two and how are they similar?

• Covariance can be broken down into correlation × the standard deviations of the two returns.

• This shows that both how closely returns move together (correlation) and how much they vary (standard deviations) matter.

Stock PXP has a beta of 1.5.  Using the CAPM and a risk free rate of 5.1%, 

what would you say is the expected return on PXP?

• CAPM says the extra return you expect (above the risk-free rate) equals beta × market premium (about 7.5%).

• For PXP, the expected return is 5.1% + (1.5 × 7.5%) = 16.35%.

If you were told that the expected future cash flows for PXP followed a growing perpetuity, and that the expected cash flows next period were $1, what would you say is the stock price for PXP? 

P = CF/(r-g)

• The discount rate (r) is the same as the expected return.

• Since the expected return is 16.35%, the price is

  • ((1/(.1635-.02)) = 6.9

 Where in the graph to the right is the idiosyncratic return on stock IEX?  That is, what would you point to and say “here is where we see the idiosyncratic risk in the stock return”?  Ditto the systematic return.

• The vertical distance between the blue dot (actual return) and the orange line (expected return based on beta) shows the idiosyncratic return — the "noise" that isn't explained by the market.

• The orange line itself (beta × (Rm - Rf)) represents the systematic return — the part of IEX’s return explained by overall market movements.