Capital Allocation Flashcards
The Risk-Free Asset
• Only the government can issue default free bonds.
– Risk-free in real terms only if price indexed and maturity equal to investor’s holding period.
• T-bills viewed as “the” risk-free asset
• Money market funds also considered risk-free in practice
Passive Strategies
The passive strategy avoids any direct or indirect security analysis. Supply and demand forces may make such a strategy a reasonable choice for many investors.
A natural candidate for a passively held risky asset would be a well-diversified portfolio of common stocks such as the S&P 500.
The capital market line (CML) is the capital allocation line formed from 1-month T-bills and a broad index of common stocks (e.g. the S&P 500).
From 1926 to 2009, the passive risky
portfolio offered an average risk premium of
7.9% with a standard deviation of 20.8%,
resulting in a reward-to-volatility ratio of
.38
The Role of Diversification and Allocation
The Investment Decision, Top-down process with 3 steps:
- Capital allocation between the risky portfolio and risk-free asset
- Asset allocation across broad asset classes
- Security selection of individual assets within each asset class.
- Market risk – Systematic or nondiversifiable
- Firm-specific risk – Diversifiable or nonsystematic, which can be diversified away by increasing the number of stocks in the portfolio
- Portfolio risk depends on the correlation between the returns of the assets in the portfolio
- Covariance and the correlation coefficient provide a measure of the way returns of two assets vary
When correlation is 1 there is no diversification achieved, if it is -1 a perfect hedge is possible.
The amount of possible risk reduction through diversification depends on the correlation.
• The risk reduction potential increases as the correlation approaches -1.
– If rho = +1.0, no risk reduction is possible.
– If rho = 0, σP may be less than the standard deviation of either component asset.
– If rho = -1.0, a riskless hedge is possible.
The Minimum Variance Portfolio
- The minimum variance portfolio is the portfolio composed of the risky assets that has the smallest standard deviation, the portfolio with least risk.
- When correlation is less than +1, the portfolio standard deviation may be smaller than that of either of the individual component assets.
- When correlation is -1, the standard deviation of the minimum variance portfolio is zero.
Which CAL to choose from the opportunity set of Debt and Equity funds
Maximize the slope of the CAL for any possible portfolio, P (ie the tangental line to the efficient portfolio)
• The objective function is the slope:
risk premium over risk free/ stdev of portfolio
• The slope is also the Sharpe ratio.
From the we determine the Optimal overall portfolio by introducing indifference curve that is tangent to this CAL line
What is Markowitz Portfolio Selection Model
It is a Security Selection process
– The first step is to determine the risk-return opportunities available.
– All portfolios that lie on the minimum variance frontier from the global minimum variance portfolio and upward provide the best risk-return combinations, (ie efficient frontier)
- now, Draw the capital allocation line which is tangent at P, Everyone invests in P, regardless of their degree of risk aversion.
– More risk averse investors put more in the riskfree asset.
– Less risk averse investors put more in P.
But here is the problem
– Determination of the optimal risky portfolio is purely technical.
– Allocation of the complete portfolio to Tbills versus the risky portfolio depends on personal preference.
Optimal Portfolios and Nonnormal Returns
- Fat-tailed distributions can result in extreme values of VaR and ES and encourage smaller allocations to the risky portfolio.
- If other portfolios provide sufficiently better VaR and ES values than the mean-variance efficient portfolio, we may prefer these when faced with fat-tailed distributions.
