Unformatted text preview: oo.com/bonds/composite_bond_rates We usually use 3month Treasury bill (3M Tbill) yield
We
as the riskfree investment return (riskfree rate, or
“rf”), and its volatility (std) can be assumed = 0
”),
515
(why?)
(why?) Risk premiums (excess returns)
Why should all assets’ expected returns be higher
Why
than 3M Tbill?
than
Investors expect to receive higher returns on all
Investors
other assets as compensation for risk because
they are riskier than 3M Tbill
they
In general,
In
excess return = simple return – 3M Tbill rate,
excess
this can be called “risk premium”
this
More details will be given in Sharpe ratio and
More 516 Sharpe ratio – by William Sharpe 517 Back to risk premiums: The premium
for taking the risk
If TBill denotes the riskfree rate, rf , and variance,
If
σp , denotes volatility of returns then:
denotes
The risk premium of a portfolio (p) is: E (rP ) − rf
• Note 1: A portfolio could be one stock
• Note 2: The risk premium is the total
Note compensation for the investor to bear for all risks
on the portfolio/stock
on
518 The Sharpe (RewardtoVolatility) Ratio
portfolio risk premium
S=
standard deviation of portfolio excess return = E (rP ) − rf σP • Sharpe ratio provides a standard to measure “How
much you earn for bearing one unit of volatility
(standard deviation)”
519 Sharpe ratio for Dell using Excel
• Check the excel template: “IndexData” tab
• Let riskfree rate = 0.1% per month
Monthly DJIA NASDAQ Mean ret 0.7% 1.0% St dev. 4.3% 6.9% Risk prem. 0.6% 0.9% Sharpe 0.14 0.13 • Thus, in DJIA, we get 0.14 of risk premium per unit of volatility; in NASDAQ, we get 0.13 of risk
premium per unit of volatility
520 Exercise 4
• Now, if we short 1$ of DJIA and use the cash to buy $1 in NASDAQ
• What’s the mean return, st. dev. and Sharpe
ratio of such a portfolio?
• Ans: Mean = 0.29%, Volatility = 4.93%, Sharpe =
0.039
• Will the answer change when we short $1000 of DJIA and long $1000 of NASDAQ?
521 Capital allocation line of 1 risky asset
and 1 riskfree asset 522 A portfolio consisting of two assets: one
stock and one Tbill
rf = 7% σ f = 0% E(rs) = 15% σ s = 22% y = % in stock (1y) = % in Tbill 523 Expected Returns for Combined Portfolio
E(rp) = y E(rs) + (1  y) rf
E(rp)= expecte...
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This document was uploaded on 03/03/2014.
 Spring '09

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