Securities Analysis 3FB3 February 26 , 2014
Chapter 5: Risk Aversion and Capital Allocation to Risky Assets
5.1 Risk and Risk Aversion
Risk, Speculation, and Gambling
Speculation – the assumption of considerable business risk in obtaining commensurate gain.
To gamble is to bet or wager on an uncertain outcome.
Risk aversion and speculation are not inconsistent.
Sometimes a gamble can look like speculation. Case of differing beliefs: heterogeneous
Risk Aversion and Utility Values
A prospect with zero risk premium is called a fair game. Riskpenalty system is applied by
people based on their risk levels. Each investor can assign a utility, or welfare, score to
competing investment portfolios based on the expected return and risk of portfolios. IT can be
viewed as a means of ranking portfolios. Higher utility values are assigned to portfolios with
more attract riskreturn profiles.
We may interpret a portfolio’s utility value as its certainty equivalent ROR ▯the rate that risk
free investments would need to offer with certainty to be considered equally attractive to the
Riskneutral investors judge risky prospects solely by their expected RORs. The level of risk is
irrelevant. For this investor, a portfolio’s certainty equivalent rate is simply its expected ROR.
Indifference curve is in the meanstandard deviation graph and connects all portfolio points
with the same utility value.
5.2 Capital Allocation Across Risky and RiskFree Portfolios
Capital allocation decision is an example of an asset allocation choice – a choice among broad
investment classes, rather than among the specific securities within each asset class. Most
investment professionals consider asset allocation to be the most important part of portfolio
5.3 The RiskFree Asset
Only the government can issue defaultfree bonds. The only riskfree asset in real terms would
be a perfectly priceindexed bond. A defaultfree perfectly indexed bond offers a guaranteed real
rate to an investor only if the maturity of the bond is identical to the investor’s desired holding
period. Even indexed bonds are subject to interest rate risk. When future real rates are uncertain,
so is the future price of perfectly indexed bonds.
Tbills are viewed as “the” riskfree asset. Their ST nature makes their values insensitive to
interest rate fluctuations.
Most investors use a broader range of money market instruments as RF assets, they are virtually
free of interest rate risk because of ST maturities.
Most money market funds hold 3 types of securities: Tbills, bearer deposit notes (BDN) and
commercial paper (CP).
We treat money market funds as the most easily accessible RF asset for most investors.
5.4 Portfolios of One Risky Asset and One RiskFree Asset [Type text] [Type text] [Type text]
The base rate of return for any portfolio is the RF rate. The portfolio is expected to also earn a
risk premium that depends on the risk premium of the risky portfolio and the investor’s exposure
to the risky asset. Risk averse and won’t take on a risky position without a positive risk premium.
When you combine a risky asset and a RF asset in a portfolio, your SD of the portfolio is the SD
of the risky asset multiplied by the weight of the risky asset in that portfolio.
Slope of CAL line is risk premium / standard deviation of risky portfolio
Increasing the fraction of the overall portfolio invested in the risky asset increases the expected
return by the risk premium. It also increase portfolio SD. The extra return per extra risk is risk
premium/SD ▯the slope
Amount invested in risky is SD of total portfolio / SD of risky portfolio
Investment opportunity set ▯set of feasible expected return and standard deviation pairs of all
portfolios resulting from different values of