Portfolio Management

The relationship between risk and rate of return

The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified time. In theory, the risk-free rate is the minimum return an investor expects for any investment because he or she will not accept more risk unless the potential rate of return is greater than the risk-free rate.

In practice, however, the risk-free rate does not exist because even the safest investments carry a very small amount of risk. Thus, the interest rate on a three-month U.S. Treasury bill is often used as the risk-free rate.

The Modern portfolio theory attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently lower risk for a given level of expected return, by carefully choosing the proportions of various assets.

The assets in an investment portfolio should not be selected individually, each on their own merits. Rather, it is important to consider how each asset changes in price relative to how every other asset in the portfolio changes in price.

Investing is a tradeoff between risk and expected return. In general, assets with higher expected returns are riskier. For a given amount of risk, the MPT describes how to select a portfolio with the highest possible expected return. Or, for a given expected return, MPT explains how to select a portfolio with the lowest possible risk (the targeted expected return cannot be more than the highest-returning available security, of course, unless negative holdings of assets are possible.

Let’s assume that investors are risk-averse, meaning that given two portfolios that offer the same expected return, investors will prefer the less risky one. Thus, an investor will take on increased risk only if compensated by higher expected returns. Conversely, an investor who wants higher expected returns must accept more risk. The exact trade-off will be the same for all investors, but different investors will evaluate the trade-off differently based on individual risk aversion characteristics.

Investment diversification in an investor portfolio.

Investors can reduce their exposure to individual asset risk by holding a diversified portfolio of assets. Diversification may allow for the same portfolio expected return with reduced risk. These ideas have been started with Markowitz and then reinforced by other economists and mathematicians such as Andrew Brennan who have expressed ideas in the limitation of variance through portfolio theory.

When it comes to investing, savvy money managers advise that you spread your money around, that is, “diversify” your investments. Diversification protects you from losing all your assets in a market swoon. The sharp decline in stock prices in recent years are proof enough that putting all your eggs in one basket is a risky strategy.

But in order to diversify correctly, you need to know what kinds of investments to buy how much money to put into each one, and how to diversify within a particular investment category.

Having a lot of investments does not make you diversified. To be diversified, you need to have lots of different kindsofinvestments. That means you should have some of all of the following: stocks, bonds, real estate funds, international securities, and cash. Once you’ve diversified by putting your assets into different categories, you need to diversify again. It’s not enough to buy one stock, for instance, you need to have a lot of different types of stocks in that portion of your portfolio. That protects you from being ravaged when a single industry — say, financial services or health care — takes it on the chin.

How stocks, bonds, real estate, metals, and global funds may be used in a diversified portfolio. 

Investments in each of these different asset categories do different things for you. Stocks help your portfolio grow. Bonds bring in income. Real estate provides both a hedge against inflation and low “correlation” to stocks — in other words, it may rise when stocks fall.

Finally, International investments provide growth and help maintain buying power in an increasing globalized world. Also, cash gives you and your portfolio security and stability.

Like a great car, diversification is something that almost everybody wants but seems hard to get if you do not have a lot of money to spend. Luckily for investors, there are more options now than ever before for adding diversity to a portfolio.

The best way for an individual investor to diversify a small portfolio of stocks and funds is to buy more stocks and funds. By allocating a few slots in the portfolio to other assets classes (bonds, hard assets, real estate, etc.), other styles (growth, distressed, etc.), and other regions, investors can achieve an impressive level of diversification without stretching their capital too far. However, remember not to diversify just for diversity’s sake – give the same level of careful attention and due diligence to any asset that you are considering as an investment.

The concept of the efficient frontier. How can we use it to determine an asset portfolio for a specified investor.

The efficient frontier is a concept in modern portfolio theory introduced by Harry Markowitz and others. A combination of assets, i.e. a portfolio, is referred to as “efficient” if it has the best possible expected level of return for its level of risk (usually proxied by the standard deviation of the portfolio’s return). Here, every possible combination of risky assets, without including any holdings of the risk-free asset, can be plotted in risk-expected return space, and the collection of all such possible portfolios defines a region in this space.

The upward-sloped (positively-sloped) part of the left boundary of this region, a hyperbola, is then called the “efficient frontier”. The efficient frontier is then the portion of the opportunity set that offers the highest expected return for a given level of risk, and lies at the top of the opportunity set or the feasible set.

A set of optimal portfolios that offers the highest expected return for a defined level of risk or the lowest risk for a given level of expected return. Portfolios that lie below the efficient frontier are sub-optimal, because they do not provide enough return for the level of risk. Portfolios that cluster to the right of the efficient frontier are also sub-optimal, because they have a higher level of risk for the defined rate of return.

Since the efficient frontier is curved, rather than linear, a key finding of the concept was the benefit of diversification. Optimal portfolios that comprise the efficient frontier tend to have a higher degree of diversification than the sub-optimal ones, which are typically less diversified.

The efficient frontier concept was introduced by Harry Markowitz in 1952 and is a cornerstone of modern portfolio theory.

Economic outlook for 2013

Prospects for the global economy are slowly improving again, but growth is expected to be weak, especially in Europe, and unemployment in many advanced economies will stay high, according to the IMF’s latest forecast.

Although action by policymakers in Europe and elsewhere has helped to reduce vulnerabilities, risks of a renewed upsurge of the crisis in Europe continue to loom large, along with geopolitical uncertainties affecting the oil market.

The global economy will continue to expand, though risks from Europe and the Persian Gulf could slow expansion considerably. The International Monetary Fund’s recent World Economic Outlook predicts 3.5 percent growth in world GDP this year, 4.1 percent next year.  Both years have been revised upward since the autumn 2011 forecast.

In 2013, the world economy will do a little better than the IMF forecast, though the risks are even greater. My disagreement with the IMF forecast is within the range of normal professional differences. Their projections are certainly plausible. Business leaders could well use the IMF forecasts as their own base case projections for market potential around the world.

Turmoil in the Middle East is setting back tourism, lowering foreign investment, and putting oil revenue at risk. This region could bounce back moderately if Egypt and Syria settled their political problems. There’s probably not much of an upside scenario possible with respect to Iran, so let’s just say that a Persian Gulf war would be very harmful for much of this region.

Africa has been growing well, thanks partly to strong commodity prices and partly to the spread of good government (even though it’s still somewhat uneven). Finally, American businesses should recognize that global markets offer more growth potential than any of the 50 states.