Arbitrage Pricing Theory (APT)

A substitute and concurrent theory to the Capital Asset Pricing Model (CAPM) is one that incorporates multiple factors in explaining the movement of asset prices. The arbitrage pricing model (APT) on the other hand approaches pricing from a different aspect.   It is rarely successful to analyse portfolio risks by assessing the weighted sum of its components.  Equity portfolios are far more diverse and enormously large for separate component assessment, and the correlation existing between the elements would make a calculation as such untrue.  Rather, the portfolio’s risk should be viewed as a single product’s innate risk.  The APT represents portfolio risk by a factor model that is linear, where returns are a sum of risk factor returns.  Factors may range from macroeconomic to fundamental market indices weighted by sensitivities to changes in each factor.  These sensitivities are called factor-specific beta coefficients or more commonly, factor loadings.  In addition, the firm-specific or idiosyncratic return is added as a noise factor.  This last part, as is the case with all econometric models, is indispensable in explaining whatever the original factors failed to include.  In contrast with the CAPM, this is not an equilibrium model; it is not concerned with the efficient portfolio of the investor.  Rather, the APT model calculates asset pricing using the different factors and assumes that in the case market pricing deviates from the price suggested by the model, arbitrageurs will make use of the imbalance and veer pricing back to equilibrium levels.  At its simplest form, the arbitrage pricing model can have one factor only, the market portfolio factor. … Read the rest

Diversification of Risk in Portfolio Management

Average investors are risk averse. Therefore, they will be ready to invest into securities under the presumption of an adequate compensation for risk taking. The compensation for the risk taken should be in the form of minimal rate of return for the invested financial assets, and the rate is named the required rate of return. It has two components:

  • Delayed consumption compensation (investors could have purchased goods and services with the assets they are to invest) and
  • Risk acceptance compensation.

Diversification is used to stabilize the potential return, and thus increase the value of the investment. Diversification stands for he investment of capital into several different securities or projects, all together called the portfolio. Each security or project entails certain risk; however, the only thing that matters to the investors who diversify their investments is the total risk (portfolio risk) and the portfolio return. There are two types of risks associated with portfolio investments:

  • Systemic Risk – Risk that can be diversified and
  • Non-systemic Risk – Risk that can not be diversified.

It is a known fact that investments with a high level of portfolio diversification have more stable and higher returns in comparison to investments that do not diversify their portfolio. It should be mentioned that investments into securities entail both the systemic and non-systemic risk.

Read More About: Systematic Risk and Non-Systematic Risk in Portfolio Investments

Systemic risk cannot be suspended, i.e. it is always present, and at the securities market it is manifested as the threat of recession, inflation, political turmoil, rise in interest rates etc.… Read the rest

Different Types of Stock Beta

Beta coefficient is a comparative measure of how the stock performs relative to the market as a whole. It is determined by plotting the stock’s and market’s returns at discrete intervals over a period of time and fitting (regressing) a line through the resulting data points. The slope of that line is the levered equity beta. When the slope of the line is 1.00, the returns of the stock are no more or less volatile than returns on the market. When the slope exceeds 1.00, the stock’s returns are more volatile than the market’s returns. The beta coefficient is a key component for the Capital Asset Pricing Model (CAPM), which describes the relationship between risk and expected return and that is used in the pricing of risky securities.

The important types of stock beta used in financial analysis are historical beta, adjusted beta and fundamental beta.

An historical betas are simply the slope of a regression line between returns on a stock and returns on some market index during some past period.  Historical betas can vary significantly depending on the length of the holding period used (i.e., days, weeks, months, or years) and the number of time periods included (i.e., the number of years of data used).  There is no “theoretically correct” procedure, and what’s “theoretically correct” probably varies from investor to investor and over time for a given investor.  For example, one person might have a short time horizon and buy stocks thinking about returns over a few days or weeks, while another might buy for the “long haul” and not even check his or her results except annually, and the investor’s time horizons might change over time.… Read the rest

The Role of Portfolio Management in an Efficient Market

You have learned that a basic principle in portfolio management is the diversification of securities. Even if all stocks are priced fairly, each still poses firm-specific risk that can be eliminated through diversification. Therefore, rational security selection, even in an efficient market, calls for the selection of a well-diversified portfolio, providing the systematic risk level that the investor wants. Even in an efficient market investors must choose the risk-return profiles they deem appropriate.

The efficient market hypothesis (EMH) states that a market is efficient if security prices immediately and fully reflect all available relevant information.  If the market fully reflects information, the knowledge of that information would not allow an investor to profit from the information because stock prices already incorporate the information. In an efficient market, no securities are consistently over-priced or under-priced.  While some securities will turn out after any investment period to have provided positive alphas (i.e., risk-adjusted abnormal returns) and some negative alphas, these past returns are not predictive of future returns.

Proponents of the efficient market hypothesis believe that active management is largely wasted effort and unlikely to justify the expenses incurred. Therefore, they advocate a passive investment strategy that makes no attempt to outsmart the market. A passive strategy aims only at establishing a well-diversified portfolio of securities without attempting to find under or overvalued stocks. Passive management is usually characterized by a buy-and-hold strategy. Because the efficient market theory indicates that stock prices are at fair levels, given all available information, it makes no sense to buy and sell securities frequently, which generates large brokerage fees without increasing expected performance.… Read the rest

Modern Portfolio Theory – Markowitz Portfolio Selection Model

Markowitz Portfolio Theory

Harry Markowitz developed a theory, also known as Modern Portfolio Theory (MPT) according to which we can balance our investment by combining different securities, illustrating how well selected shares portfolio can result in maximum profit with minimum risk. He proved that investors who take a higher risk can also achieve higher profit. The central measure of success or failure is the relative portfolio gain, i.e. gain compared to the selected benchmark.

Modern portfolio theory is based on three assumptions about the behavior of investors who:

  • wish to maximize their utility function and who are risk averse,
  • choose their portfolio based on the mean value and return variance,
  • have a single-period time horizon.

Markowitz portfolio theory is based on several very important assumptions. Under these assumptions a portfolio is considered to be efficient if no other portfolio offers a higher expected return with the same or lower risk.

  1. Investors view the mean of the distribution of potential outcomes as the expected return of an investment.
  2. Investors view the variability of potential outcomes about the mean as the risk of an investment. Variability is measured by variance or standard deviation.
  3. Investors all have the same holding period. This eliminates time horizon risk.
  4. Investors base all their decisions on expected return and risk. By connecting all the points of equal utility, a series of curves called the investor’s indifference or utility map is created.
  5. For a given risk level, investors prefer higher returns to lower returns, or for a given return level, investors prefer less risk to more risk.
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Investments When Entire Stock Market Is Under Or Over Valued

Should management proceed with investing in a project with a satisfactory NPV (Net Present Value) if it has sufficient funds to do so, and if (a) the entire stock market is significantly undervalued and may well rise by 25 or 30% over the next year, or (b) the entire stock market is significantly overvalued and may well fall by 25 or 30% over the next year?

In case (a), it could be argued that management should postpone the investment for a year, and invest the cash in a general portfolio of shares, realize them after a year, then take up the postponed investment, and use the capital gain either for future investment or a special dividend payment to shareholders. However, most shareholders do not expect or want the company to use their money for speculative share investments since most companies are unlikely to possess the appropriate skills to do so. Imagine if the market went down instead of up! Thus, a speculative investment should be considered as inappropriate for all but specialist investment companies. Having removed this possibility, we should, however, consider whether there is any advantage in postponing the investment until shares have risen by the expected amount. Unless the postponement would result in a higher present NPV due to the actual rise in share prices, the company should not postpone the investment. It is noted that a higher NPV due to the rise in share prices is not likely to occur: it means that the rise would create a better market for the project’s output.… Read the rest