Investment Theory and Portfolio Development - Modern Portfolio Theory (MPT)
There is a natural trade-off between risk and return which is positively correlated. Standard deviation is the measure of total risk or volatility of returns over time. Investors seek efficient asset mixes, known as portfolios, which maximize return for a given level of risk or minimize risk for a given level of return. What follow are some of the kernel concepts of modern portfolio theory.
- Capital Market Line (CML)-is the graphic depiction of the risk/return relationship for efficient portfolios. It is a macro perspective on the risk and return relationship. The continuum plots the risk/return profile of numerous portfolios created by combining various proportions of equities and cash. The implication of the model is that investors should be compensated with greater return for assuming greater risk. The Capital Market Line formula reads as follows:
Rp=Rf+(Rm-Rf/σm)σp where Rp=return on the portfolio; Rf=risk-free rate; Rm-Rf=risk premium; σm=standard deviation of the market; σp=standard deviation of the portfolio. Know this formula, its implications for MPT and for securities valuation.
- Mean-variance optimization - the quantitative tool that enables investors to construct portfolios that attempt to achieve maximum return for a given level of risk given their portfolio constraints.
- Efficient Frontier - the asset allocation along the risk continuum that represents the highest possible expected return for a given level of risk or the lowest level of risk for a given expected return.
- Security Market Line (SML) - the line graphs the inputs of the CAPM. As distinct from the capital market line, the security market line is used to plot the risk and return relationship both for portfolios of individual securities and the individual securities themselves. The SML represents the required return on a security which may (not) equal its actual return, depending upon the degree to which markets are in disequilibrium. Alpha is the difference between the security's actual vs. required return. Undervalued securities' forecast returns lies above the SML, that of overvalued securities below it. The SML formula reads as follows. Candidates will note that it is the formula for the Capital Asset Pricing Model (CAPM).
Rs(p)=Rf+β(Rm-Rf) where Rs(p)= return on the portfolio or security, Rf= risk-free rate; Rm= return on the market. CAPM is central to equity valuation.
An example will illustrate the application of the CAPM. Wilfredo holds a diversified portfolio that returned 18.32% last year. In the same year, the market returned 13.89%. The portfolio's risk-free rate was 5.2% and the beta for Wilfredo's portfolio was 1.42. Did his portfolio perform well on a risk-adjusted basis?
Using the inputs in the CAPM model, we learn that 0.052+1.42(.139-.052) =.176
Wilfredo's portfolio returned 18.32%, which is a bit better than the expected return of 17.6% from CAPM. Conclusion: Wilfredo's portfolio outperformed the market on a risk-adjusted basis as the forecast return exceeded the required return as calculated by the SML formula.