¶ … risk and return for an investment portfolio that includes five asset categories: stocks, bonds, mutual funds, options, and precious metals. The purpose of diversified portfolio investment is to maximize portfolio expected return for a given level of risk, or to minimize risk for a specific level of expected return. This paper reviews mathematical formulae for modeling risk and return which provide a rationale for investment strategies and portfolio management. The paper also discusses risk and return objectives and expectations, along with investment risk profiles.
Risk vs. Return Measurement
In an ideal world, the typical investor would select investments whose attributes include high returns coupled with low risk. In reality, there are few of these kinds of investments available, consequently financial managers have gone to great lengths to develop methods and strategies that allow them to come as close as possible to selecting the ideal investment. One such financial theory for managing portfolio risk is modern portfolio theory (MPT), which I used to determine portfolio risk vs. return measures. Other measures of portfolio performance include the capital asset pricing model of William Sharpe and John Litner, as well as Treynor and Sharpe indices.
Developed by Harry Markowitz and published under the title "Portfolio Selection" in the 1952 Journal of Finance, MPT is considered one of the most important and influential economic theories dealing with finance and investment. MPT posits that it is not enough to look at the expected risk and return of a particular stock, and argues that by investing in more than one stock, the investor benefits from diversification, thereby reducing the riskiness of the portfolio. In most investment scenarios, the risk that investors take when they buy a stock is that the return will be lower than expected, deviating from the average return (McClure, 2011).
MPT recognizes that each stock has its own standard deviation from the mean, which MPT defines as risk. Markowitz demonstrated that the risk in a portfolio that contains diverse individual stocks will be less than the risk inherent in holding any one of the individual stocks (assuming the risks of the various stocks are not directly related.) Markowitz showed that successful investing requires more than selecting stocks, that it requires choosing the correct combination of stocks (Ibid).
MPT distinguishes between the two components of risk that accompany individual stock returns. Systematic risk, such as interest rates, recessions and war, are market risks that cannot be diversified away; while unsystematic risk that is specific to individual stocks can be diversified away as one increases the number of stocks in a portfolio. Specific risk represents the component of a stock's return that is not correlated with general market moves. In a well-diversified portfolio, the covariance between individual stock's levels of risk determines overall portfolio risk. Consequently, investors benefit from holding diversified portfolios instead of individual stocks (Ibid).
To establish risk measures, one can use the efficient frontier to identify the best level of diversification. At every level of return, there is one portfolio that offers the lowest possible risk, and conversely, for every level of risk, there is a portfolio that offers the highest return. Plotting these combinations on a graph produces a line that defines the efficient frontier. Any portfolio that lies on the upper part of the curve is efficient, and provides the maximum expected return for a given level of risk. The rational investor only holds a portfolio that lies somewhere on the efficient frontier (Ibid).
Investors often use the rate of return of a risk-free asset as a benchmark to measure the return of the other financial assets. Investment analysts typically pick a U.S. Treasury security as a representation of a risk-free asset, with the two most popular choices being the 3-month T-bill and the 30-year T-bond. Many analysts and investors, including this one, favor the 30-year T-bond because it reflects the investment horizon of most investors, even though it is more sensitive to interest rate and inflation changes (Wan, n.d.).
Other benchmarks include:
The Dow, S&P 500, and Nasdaq Composite for stocks and mutual funds
Lehman Brothers Global Aggregate Bond Index for bonds
CBOE DJIA BuyWrite Index for options
UBS Bloomberg CMCI Precious Metals Index for precious metals
Benchmarks provide a standard against which an investment or investment manager can be measured.
The risk-free rate represents the lowest level of return that an investor expects to receive, and as an investor takes on more risk (relative to a risk-free-asset) he/she will ask for a higher return. Therefore the expected return of a risky asset is calculated as follows:
E (Rr) = Rrf + [E (Rr) -- Rrf]
= Minimum compensation + compensation for taking additional risk (i.e. risk premium)
where Rrf, the risk-free rate, represents the minimum compensation an investor can expect to receive, and the second component measures the difference...
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