bkm6: risk aversion & capital alloc Flashcards
different appetites (tolerance) for risk
Risk averse investors prefer lower risk. They require a risk premium as
compensation for the risk borne.
Risk neutral investors ignore risk and base decisions only on expected return
Risk lovers prefer investments with a higher level of risk, and will in fact be
willing to accept a lower return to gain a higher level of risk.
Utility
amount of benefit, depends on multiple factors (risk appetite, expected return, risk level)
U = E(r) - 0.5Aσ^2
A = degree of the investor’s risk aversion
certainty equivalent rate
rate that a risk free investment
would need to offer to provide the same level of utility as the investment being analyzed
expected return and std dev of return for a complete portfolio (with risk free assets and risky assets) where portion invested in risky assets P = y
ie E[rc] & σc
Capital Allocation Line, CAL
graph showing risk and return levels of various investment options available to investor based on distribution of complete portfolio
where does portfolio lie on CAL when investor borrows at the risk free rate, and invests the proceeds in P
portfolio will lie on the CAL to the right of P
slope of the CAL
This is called the reward-to-volatility ratio, or Sharpe ratio. It represents the
incremental return per unit of standard deviation.
The CAL needs to be adjusted to reflect the fact that in reality, normal investors can not borrow at the risk free rate
CAL will be kinked at P
the slope to the right of P will be
Optimal Complete Portfolio, C and y*
investor will select portfolio that maximizes utility,
y* is optimal ratio and is derived by setting derivative of utility equation to 0
indifference curves
curves that contain different portfolios that the
investor is indifferent about (portfolios with equivalent utility levels)
optimal risky portfolio can also be derived graphically
need to plot indifference curves
An investor prefers to be on the highest possible indifference curve: this would be the highest indifference curve that touches the CAL. The optimal portfolio is located at the intersection point of the CAL, and the curve tangential to the CAL
risky portfolio P can be determined by either
active or passive strategy
Nonnormal Returns and capital allocation to risky portfolio
if the returns are more heavy tailed than a normal distribution would imply, it may be more appropriate to reduce the allocation to the risky portfolio
this is because using indifference curves uses the standard deviation as the measure of risk, as it assumed that returns follow a normal distribution
active vs passive strategy
Capital Market Line, CML
CAL that uses passive portfolio as risky portfolio
