Core Concepts

1. In theory, there is a fundamental tradeoff between risk and return-the higher the expected return, the higher the risk.

2. If markets are very efficient (i.e., prices reflect all relevant information), the fundamental tradeoff between risk and return will hold.

3. Historical time-series statistics on the U.S. stock market:

• Average annual return = 10% (Daily average return is very close to zero)
• Daily standard deviation = 1% (Annual standard deviation = 20%) 

4. If George tells you what stocks/assets to buy/sell, you need to ask three questions:

• If George has found such a great strategy, why is he telling me?  In particular, what's in it for George?  How does George get paid? 
• Why does this strategy work?  Where is the inefficiency?  Why does the fundamental tradeoff between risk and return break down? (people behave irrationally, stale prices, etc.) 
• When other investors learn about the pattern, will this strategy keep working?  

5. Diversification--when stocks are less than perfectly correlated, you can reduce the standard deviation of a portfolio by increasing the number of stocks in the portfolio. Diversification works because when correlation is less than 1, the standard deviation of portfolio returns is less than the weighted average of the individual stocks' standard deviations. Only firm-specific risk can be diversified away.

6. The Capital Asset Pricing Model yields the following pricing equation, corresponding to the SML (security market line):

E(r_i) = r_f + ß_i [ E(r_m) - r_f ]

This equation means that only systematic risk is priced (so that there is a fundamental tradeoff between expected return and systematic risk).

7. The next two core concepts (put-call parity and the Black-Scholes formula) are derived as follows. You form a portfolio using options and the underlying stock so that the payoff at expiration is known today with certainty. Consequently, the amount you would be willing to pay for that portfolio is equal to the amount that you would be willing to pay for a risk-free T-bill or T-bond that has the same time to maturity and gives the same payoff.

8. Put-call parity establishes the relationship between put and call premiums (on the same underlying stock, with the same time to maturity, with same exercise price) at a given point in time:

S₀ + P₀ - C₀ = PV(X)

9. The Black-Scholes option pricing formulas for call and put options on a stock that pays no dividends are

C₀ = S₀N(d₁) - Xe^-rTN(d₂),      P₀ = S₀[N(d₁)-1] - Xe^-rT[N(d₂)-1]

where     and   

 
Contents written by Jason Karceski
Last modified on December 02, 2007.