Markowitz Portfolio theory

The Investment Process

It is rare to find investors investing their entire savings in a single security. Instead, they tend to invest in a group of securities. Such a group of securities is called a portfolio. Financial experts stress that in order to Security Analysis and Portfolio

minimise risk an investor should hold a well-balanced investment portfolio. The investment process describes how an investor should decide the securities to invest in while constructing a portfolio, how he should spread the investments, and when he should sell them. This is a procedure involving the following five steps:

1. Setting investment policy

This initial step determines the investor’s objectives and the investible amount. Since there is a definite relationship between risk and return, the objectives should be stated in terms of both risk and return.

This step concludes with the asset allocation decision, which is identification of the potential categories of financial assets for consideration in the portfolio that the investor is going to construct. Asset allocation Security Analysis and Portfolio Management involves dividing an investment portfolio among different asset categories, such as stocks, bonds and cash.

The asset allocation that works best for an investor at any given point in his life depends largely on his time horizon and his appetite for risk.

Time horizon – The time horizon is the expected number of months, years, or decades for which the money will be invested. An investor with a longer time horizon may feel more comfortable with a riskier or more volatile investment because he can ride out the economic cycles and the inevitable difficulties of the markets. But an investor, saving for his teenage daughter’s college education would be less likely to take a large risk because he has a shorter time horizon.

Risk appetite – Risk appetite is an investor’s ability and willingness to lose some or all of his original investment in exchange for greater potential returns. An aggressive investor with greater risk tolerance is more likely to risk losing money in order to get better results. A conservative investor will favour investment that protects his original investment. Conservative investors keep a "bird in the hand”, while aggressive investors seek "two in the bush."

While setting the investment policy, the investor also selects the portfolio management style (active vs. passive management).

Active management is the process of managing investment portfolios by attempting to time the market and/or select undervalued stocks to buy and overvalued stocks to sell, based upon research, investigation and analysis.

Passive management is the process of managing investment portfolios by trying to match the performance of an index (such as a stock market index) or asset class of securities as closely as possible, by holding all or a representative sample of the securities in the index or asset class. This portfolio management style does not use market timing or stock selection strategies.

2. Performing security analysis

The second step is security selection. Security analysis involves examining a number of individual securities and identifying those securities that currently appear to be mispriced. Security analysis is done using Security Analysis and Portfolio Management fundamental or technical analysis or both Fundamental analysis is a method used to evaluate the worth of a security by studying the financial data of the issuer. It scrutinises the issuer's income and expenses, assets and liabilities, management, and position in its industry. In other words, it focuses on the ‘basics’ of the business.

Technical analysis is a method used to evaluate the worth of a security by studying market statistics. Unlike fundamental analysis, technical analysis disregards an issuer's financial statements. Instead, it relies upon market performance of the scrip to ascertain investor sentiment.

3. Portfolio construction

The third step identifies the specific assets in which to invest, and determines the amounts to put into each asset. Here selectivity, timing and diversification issues are addressed. Selectivity refers to security analysis and focuses on price movements of individual securities. Timing involves forecasting of price movement of stocks relative to price movements of fixed income securities (such as bonds). Diversification aims at constructing a portfolio that minimises the investor’s risk.

Common Errors in Investment Management

When investment mistakes happen, money is lost. Mistakes can occur for a variety of reasons, but they generally happen because of the clouding of the investor’s judgment by the influence of emotions, not applying basic investment principles, or misconceptions about how securities react to varying economic, political, and fear-driven circumstances. The investor should always keep a rational head and avoid these common investment mistakes:

 Not having a clearly defined investment plan

A well-planned investment strategy does not need frequent adjustments, and there is no place in it for speculations and “hot picks”. Investing is a goal-oriented activity that should consider time, risk appetite and future incomes.

 Becoming complacent and abandoning the plan

Changing direction frequently and making drastic rather than measured adjustments is a serious mistake. Always regard investing as a long-term activity.

 Emotional attachment to securities that rise and not booking profits

Profits that are not realised are just book profits and may disappear when the market goes down. While one should not be in a hurry to realise profits, it is equally erroneous to be blind to the beauty of unrealized gain and forget basics of prudent investing. Some investors may have “unwilling-to-pay-the-taxes” problem, little realising that the investment may ultimately end up as a realised loss on the tax return.

 Overdose of market information

Investors sometimes suffer from "paralysis by analysis" and become confused and indecisive. Aggravating this problem for the investor is his inability to distinguish between genuine research and sales pitch of the sale side analyst. A narrow focus on information, which has a bearing on the investment, is far more productive and useful.

 Looking for the proverbial ‘quick buck’

Investors who want instant success with minimum effort buy every new instrument that catches their fancy. Their portfolios become a motley mixture of many types of securities that are simply strung together without a plan.

The Concept of Portfolio Analysis and Diversification of Risk

Harry Markowitz in the 1950s developed a theory of portfolio choice that dealt with the households' and firms' investment in financial assets under uncertainty.

A basic tenet of Economics is that due to the scarcity of resources all economic decisions involve trade-offs. Markowitz identified the trade-off facing the investor as the one between risk and expected return. (Markowitz took standard deviation of returns, also known as volatility, as a measure of risk).

Markowitz’s theory analyses how wealth can be optimally invested in portfolios which are made up of assets with different expected returns and risks. At the heart of Markowitz’s analysis is the insight that while the return on a portfolio composed of risky assets is the value-weighted average of each risky asset’s return, the risk of the portfolio is not a linear, weighted average value. The risk of a portfolio depends not only on individual variances of the different assets comprising the portfolio but on the pair-wise covariances between them.

The lower the covariances between assets (i.e. the lesser the correlation between their returns) the lower is the risk of the portfolio composed of these assets. This makes it possible to reduce the risk of a portfolio by diversification. Markowitz showed that diversification can reduce the risk of a portfolio by including in assets whose returns have low correlation with each other.

Markowitz's work compels investors to consider the relationship between individual securities’ returns.

Stocks influenced by similar industry-wide conditions will all move together in step. While in good times they all will perform well, during bad times they all will perform badly and adversely affect the portfolio’s value and return. Markowitz was the first to formally prove this intuitive finding. He showed that imperfect correlation between securities in the portfolio is the key reason why diversification reduces portfolio risk.

Accordingly he proposed that investors should focus on selecting portfolios based on their overall risk-reward characteristics rather than merely Security Analysis and compiling portfolios from securities that individually had attractive risk-reward characteristics. In a nutshell, inventors should select portfolios and not individual securities.

Assumptions of Markowitz Model

Markowitz’s model identifies the trade-off facing the investor as one between expected return (mean) and risk (variance). It makes the following assumptions concerning the investment market and investors’ behaviour in those markets.

 All investors have the same expected single period investment horizon. At the beginning of the period, the investor allocates his wealth among various assets, assigning a non-negative weight to each asset. During the period, each asset generates a random rate of return so that at the end of the period, his wealth has been changed by the weighted average of the returns.

 Investors are rational and behave in a manner so as to maximise their utility. They seek to maximise the expected return of total wealth.

 Investors base decisions on expected returns and risk (variance or standard deviation of these returns from the mean). They are risk-averse and try to minimise the risk and maximise return. They prefer higher returns to lower returns for a given level of risk.

 Investors have free access to fair and correct information on the returns and risk. All markets are perfectly efficient.

 There are no taxes and no transaction costs.

Efficient Frontier or Efficient Set

Efficient frontier represents the trade-off between risk and expected return faced by an investor when forming his portfolio. Efficient frontier was first defined by Harry Markowitz as part of his portfolio theory considers a universe of risky investments and explores what might be an optimal portfolio based upon investments in these risky securities.

Assume a one-year holding period for investment in these securities. Today's values for all the risky investments are known. The returns on these investments (reflecting price changes, coupon payments, dividends, stock splits, etc.) till the end of the holding period are random. So we can calculate expected returns and variances of returns for these securities.

Correlation of returns between individual pairs of securities must then be calculated. Using these inputs, we then calculate the expected return and variance of the portfolio as a whole. The notion of ‘optimal portfolio’ can be defined in one of two ways:

1. For any level of volatility consider all the portfolios which have that volatility (standard deviation). From among them all, select the one which has the highest expected return.

2. For any expected return, consider all the portfolios which have that expected return. From among them all, select the one which has the lowest volatility.

Each definition produces a set of optimal portfolios. Definition (1) produces an optimal portfolio for different levels of risk. Definition (2) produces an optimal portfolio for different levels of expected return. The set of optimal portfolios obtained using either definition is exactly the same and is called the efficient frontier.

In the following diagram, numerous portfolio combinations of all the available assets have been plotted. This is the attainable set of portfolios. The y-axis represents the expected return and the x-axis represents the total risk as measured by standard deviation,). From this attainable set of all possible portfolios, we locate the subset known as the efficient set which is composed of portfolios that offer the lowest risk for given level of return (or alternatively, the highest return for a given level of risk). This is the curved line EF shown in the diagram. All other portfolios in the attainable set are dominated by the efficient set. Thus the Markowitz portfolio selection model generates a frontier of efficient portfolios which are equally good. An Security Analysis and investor selects the single portfolio from this ‘efficient’ set that meets his needs.

The Markowitz efficient frontier is usually composed only of portfolios as only portfolios benefit from diversification. Individual assets contain both diversifiable and non-diversifiable risk and are generally not efficient investments. However, the most efficient portfolio may sometimes consist of a single security if it is the only way the investor can obtain the desired return with a given amount of risk.

Criticism of Markowitz Model

The Markowitz model was a brilliant innovation in the field of portfolio selection. Markowitz showed us that all the information that was needed to choose the best portfolio for any given level of risk is contained in three simple statistics, which are mean of securities’ returns, standard deviations of returns and correlation between securities’ returns.

The model requires no information about dividend policy, earnings, market share, strategy, and quality of management. In short, Harry Markowitz fundamentally altered the thinking on investment decisions. Today almost every portfolio manager uses the basic framework of the risk-return trade-offs even if they do not adopt the Markowitz model entirely.

Why does not then everyone use the Markowitz model to solve their investment problems? The answer lies in the statistics that are required as inputs for the model. The historical mean return of securities may be a poor estimate of their future mean return. As we increase the number of securities, we increase the number of correlations that we must estimate and they must be estimated correctly to obtain the right answer.

In fact, with more than thousands of stocks listed on the BSE and NSE, it is almost certain that we will find correlations that are widely inaccurate for the purpose of estimating future correlations. Unfortunately, the Markowitz model does not deal well with incorrect inputs. That is why the model is best applied to allocation decisions across asset classes (such as between stocks and bonds). For these the number of correlations is low, and the statistics (mean, standard deviation and correlation) are well-estimated.

Meaning of Risk

Risk is the likelihood that your investment will either earn money or lose money. It is the degree of uncertainty regarding your expected returns from your investments, including the possibility of losing some or all of your investment. Risk includes not only adverse outcomes (lower returns than expected) but good outcomes (higher returns). Both downside and upside risks are considered while measuring risk.

 Measurement of risk

The thumb rule for all investments is smaller the risk smaller the return; and higher the risk, higher the return. Higher returns compensate for the percent of risk taken. The risk is dependent largely on your risk appetite, which in turn changes with your age, personality and environment. The daily fluctuations of the market tend to smoothen out your long term investment (Historically the stock market has always shown a gradually increasing trend irrespective of short-term declines). But when you are old or close to your monetary goal, you cannot afford to make losses.

Investing in equity because they could give the highest returns automatically increases the risk coefficient. You may gain substantially when the markets are buoyant, but run the risk of losing your entire capital if market tumbles. If you put all your savings in ‘safe and familiar’ investments you may only earn fewer returns in the long run. For example a 7% assured rate of return which looks attractive today may not be profitable due to rising inflation or taxes. An investor always likes to yield higher returns. For that you must be prepared to take the risk of trying out various investment options.

Risk is commonly measured using variance, standard deviation and beta. Variance is the mean of the square of deviations of individual returns around their average value. Standard deviation is the square root of variance. Beta reflects the volatility of the returns in relation to market movements.

 Factors that affect Risk

The common risk factors are:

 Business risk: As a security holder you get dividends, interest or principal (on maturity in case of securities like bonds) from the firm. But there is a possibility that the firm may not be able to pay you due to poor financial performance. This possibility is termed as business risk. The poor financial performance could be due to economic slowdown, poor demand for the firm’s goods and services and large operating expenses. Such a performance affects the equity and the debt holder. The equity holder may not get dividends and residual claim on the income and wealth of the firm. Similarly a debt holder may not get interest and principal payments.

 Inflation risk: It is the possibility that the money you invested will have less purchasing power when your financial goal is met. This means, the rupee you get when you sell your asset buys lesser than the rupee you originally invested in the asset.

Interest rate risk: The variability in a security’s return resulting from changes in the level of interest rates is referred to as interest rate risk. For example the value of a bond may reduce due to rising interest rates. When the interest rate rises, the market price of existing fixed income securities fall, and vice versa. This happens because the buyer of a fixed income security would not buy it at its par value or face value if its fixed interest rate is lower than the prevailing interest rate on a similar security. This occurs due to interest fixed rate lower being lower than the present rate on a similar security. Hence as a buyer you would pay less than the face or par value for such a security. The changes in interest also have an indirect effect on effect equity prices. That means the prices are affected by changes in the relative yields of debentures.

 Market risk: Market risk is the changes in returns from a security resulting from ups and downs in the aggregate market (like stock market). This type of risk arises when unit price or value of investment decreases due to market decline. The market tends have a cyclic pattern. John Train says “You need to get deeply into your bones the sense that any market, and certainly the stock market, moves in cycles, so that you will infallibly get wonderful bargains every few years, and have a chance to sell again at ridiculously high prices a few years later”.

The market risk represents a part of the total risk of a security that can be attributed to economic factors like government spending, GDP growth rate money supply, inflation and interest rate structure. Market risk is unavoidable as the economic factors have an effect on all firms to some degree. Market risk is therefore known as systematic risk or non-diversifiable risk.

Risk Preference

An investor with a certain risk tolerance and information on the expected return and standard deviation decides on various investments. Usually investors want to invest in securities which give higher returns at lower standard deviations. According to diminishing marginal utility, as a person gets additional wealth his utility for it increases at a declining rate.

A risk-averse investor will choose Investments with the least standard deviation from a bunch with equal rates of return, or investments with the highest return from a bunch with equal standard deviations.

A risk-seeking investor likes investment with higher risk irrespective of the rate of return. In reality, most investors are risk-averse.

Risk Premium =f (Business risk, Financial Risk, Liquidity risk, Exchange risk, Country risk)

(or)

Risk Premium =f (Systematic Market Risk)

Risk Preference

Normal Distribution and Standard Deviation

The normal distribution is a bell shaped curve that is smooth, symmetric and continuous without skewness. The spread of the normal distribution is characterised by the standard deviation. What is the probability of obtaining a return exceeding or lower than the expected (mean) return? In case of normally distributed returns, it depends only on the standard deviation. It is useful to notice certain properties of a normal distribution.

 The area under the curve sums to 1.

 The curve reaches its maximum at the expected value (mean) of the distribution and one-half of the area lies on the either side of the mean.

 Approximately 50 percent of the area lies within  0.67 standard deviations of the expected value; about 68 percent of the area lies within  1.0 standard deviations of the expected value; 95 percent of the area lies within  1.96 standard deviation of the expected value and 99 percent of the area lies within  3.0 standard deviation of the expected value.

The normal probability table can be used to determine the area under the normal curve for various standard deviations. The probability of occurrence can be read from the normal probability table. This table is the ‘right tail’ of the distribution; that is probabilities of the unknown quantity being greater than X standard deviations from the expected value (mean) are given in the table. The distribution tabulated is a normal distribution with mean zero and standard deviation of 1. Such a distribution is known as standard normal distribution. However, any normal distribution can be standardised and hence the table of normal probabilities will serve for any normal distribution.The formula to standardise is:

S = R- E (R )/σ

R is the outcome (return) in which we are interested, E (R) is mean or expected return and S is the number of standard deviations from the expected return.