Risk

1
Risk

• Risky return
• This notation means realized returns may take on
  different values (ie. D and P are risky therefore
  r is risky).

2
Risk

• Eg. Suppose a stock pays no dividends and
  tomorrows price is determined on the basis of
  the flip of two coins. Todays price is 900 and
  tomorrows price is 1000 x ( heads).
• This stock is risky.
• We dont know what tomorrows price will be but
  we do know what it can be.

3
Risk

• Price can take on three possible values with
  different probabilities for each value.

4
Risk

• We also know the distribution of the stocks
  returns
• eg. What is the probability that the above
  stocks return is negative?

5
Risk

• In reality a stocks return may take on any value
  and its distribution of returns is subjective
  (ie. Its based on beliefs).
• Eg. What does the probability distribution of
  Dell returns look like?
• Risk will have to be related to the distribution
  of returns.

6
Risk

• More risky returns demand higher expected
  returns
• Expected Stock Return riskless rate risk
  premium
• BUT - how do we measure risk?

7
Some Statistics

• We need to calculate expected return and variance
  of stock returns

8
Risk

• From previous example

9
Properties of E() and Var()
10
A Simple Portfolio

• Eg. Suppose we combine the stock above with a
  t-bill one-year t-bill which is yielding 5. What
  is the mean, variance and standard deviation of a
  portfolio where 70 of the investment is in the
  stock and 30 is in the t-bill?

11
A More Complicated Portfolio

• Eg. Suppose we combine the SP 500 index with a
  t-bill one-year t-bill which is yielding 5. What
  is the mean, variance and standard deviation of a
  portfolio where 70 of the investment is in the
  index and 30 is in the t-bill? The market risk
  premium is 5 and the annual standard deviation
  is 20.

12
Diversification

• Everyone has a company - generate one of two
  payouts by tossing a coin
• H - payout110
• T - payout 105
• Whats expected payout?
• Whats variance of payout?

13
Diversification

• Suppose the riskless rate is 7. How much should
  each company cost?

14
Diversification

• If I invest an equal amount in each company, my
  return will be
• Can reduce variance by diversifying.
• How much can you reduce variance here?

15
Diversification

• If stock prices are not perfectly correlated, we
  can reduce variance by combining them into
  portfolios.

Portfolio Variance
Number of Stocks in Portfolio
16
Diversification

• Only non-diversifiable risk matters.
• This means covariance or correlation (NOT
  variance) is what matters.

17
Portfolios of Risky Assets
18
Properties of Covariance
19
Portfolios of Risky Assets

• Suppose we invest 120 in IBM stock and 180 in
  Bristol-Myers stock.
• Determine the portfolio mean. (?BM21, ?IBM17)
• Determine the portfolio standard deviation.
  (?BM21, ?IBM31, ?0.135)

20
A Simple Method for Calculating Portfolio
Covariance
21
Example

• Calculate the expected return and variance of a
  portfolio with 1000 invested in each of XOM, WMT
  and AMZN.

22
Diversification

• Only non-diversifiable risk matters.
• This means covariance or correlation (NOT
  variance) is what matters.
• Correlation with what?