¶ … 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...

This difference between the expected return of a risky security and a risk-free security is termed the risk premium of the risky security (Wan, n.d.).
In addition to looking at levels of return, investors should also analyze risk measures to assess the performance of a stock or stock fund compared to its benchmark index. Risk measures are defined as statistical measures which are historical predictors of investment risk and volatility; they are also major components in modern portfolio theory. There are five principal risk measures:

Alpha: Measures risk relative to the market or benchmark index

Beta: Measures volatility or systemic risk as compared to the market or benchmark index

R-Squared: Measures the percentage of an investment's movement that is attributable to movement in its benchmark index

Standard deviation: Measures how much return on an investment is deviating from the expected normal or average returns

Sharpe ratio: Provides an indicator of whether an investment's return is due to smart investing decisions or a result of excess risk (Risk measures, 2011).

Definition of Risk and Return Objectives

As part of the process of determining an appropriate asset allocation strategy, investment analysts recommend identifying investment objectives and preferences. Several factors determine asset allocation mix: investment stage, portfolio size, time horizon, total return objectives and risk tolerance (Piazza, n.d.).

Investment stage is described in terms of one's life cycle. During one's working or accumulation years, growth-oriented strategies are appropriate to attain higher total returns than income-oriented strategies. As one approaches retirement, possibly a more balanced-oriented strategy is appropriate to conserve accumulated assets. In one's retirement, income and stability would most likely be priorities, although some amount of growth is desirable to help protect against inflation (Ibid).

Portfolio size refers to the amount of money in one's portfolio. Obviously the higher the dollar amount, the more diversification is possible (Ibid).

Time horizon refers to the number of years in one's investment strategy. Investment objectives will vary depending upon when one withdraws all or most of the funds.

Short-term: 1 -- 3 years

Intermediate term: 3 -- 5 years

Long-term: over 5 years

Return objectives with respect to investment strategy consist of capital growth potential and current income or yield:

Growth-oriented: emphasizes capital growth over current income, appropriate for a long-term horizon only

Balanced-oriented: equal blends of capital growth and current income, appropriate for intermediate or long-term time horizons

Income-oriented: emphasizes current income over capital growth, appropriate for any time horizon (Ibid)

Risk tolerance is associated with the degree of volatility or price fluctuations in the assets, with fluctuations ranging from stable to very volatile. As risk increases, both volatility and total return potential increase proportionately; conversely lower levels of risk indicate less volatility and lower total return expectations. As long as one takes into account certain time horizon restrictions, a conservative, moderate or aggressive risk tolerance can match with any growth, balanced, or income-oriented return objective:

Conservative -- Accepts lower returns to minimize risk

Moderate -- Accepts average price fluctuations to pursue higher returns

Aggressive -- Accepts above average price fluctuations to seek above average returns (Ibid).

Rationale Behind Risk and Return Expectations

To determine my risk and return expectations, I researched using an investment questionnaire along with a scoring tool. Investment managers use such questionnaires to assess investors' risk and return expectations. There are typically five to seven risk categories to determine how the investor feels about risk, how much downside market fluctuations can be tolerated, and how much profit the investor expects to make when markets are going up. Once an investor is classified into one of several defined categories, the investment advisor uses asset allocation models that correspond directly with each category (Five most commonly-used, 2011).

I meet the definition of a moderately conservative investor, someone who can tolerate a little more risk than a conservative investor, but is still averse to large short-term downside fluctuations. I want a little more return with a little less income. The typical investor in this category is either retired and getting their paycheck from portfolio income, or soon to be retired, or like me, has been burned by poor investment management and lost a lot of money in the past. Moderately conservative investors want to be protected somewhat from large downside market fluctuations, and are willing to not fully participate when the markets rally upwards (Ibid).

The moderately conservative investor's portfolio will still…