1. In the chronological development of modern financial management, portfolio theory came first with Markowitz in 1952. It was not until 1964 that William Sharpe derived the Capital Asset Pricing Model (CAPM) based on Markowitz’s portfolio theory. For example, a key assumption of the CAPM is that investors hold highly diversified portfolios and thus can eliminate a significant proportion of total risk. The CAPM was a breakthrough in modern finance because for the first time a model became available which enabled academics, financiers and investors to link the risk and return for an asset together, and which explained the underlying mechanism of asset pricing in capital markets. For anyone making an investment decision and trying to determine what return they should require for assuming a given level of risk the CAPM seemed to have come up with the answer. The capital asset pricing model (CAPM) demonstrated how risk and return could be linked together and specified the nature of the risk-return relationship for any security or asset. The impact of the capital asset pricing model (CAPM) has been immense and it is one of the most influential financial concepts in recent financial management history. It is the basic theory which links together relevant risk and expected return for any security.
The CAPM was the first method of formally expressing this risk-return relationship: it brought together systematic risk and return for all assets. However, before analysing the basic constructs of the CAPM we need to understand a little more about the various types of investment risk.
2. Beta is a measure of the volatility of a security or a portfolio in contrast to the market as a whole.
Historical beta - the past standard deviation of a security that is employed in security analysis. Standard deviation measures the alterations in the historical price of a security. Recall that the standard deviation, σ, is used to measure an asset or share’s total risk, while the beta coefficient, β, in contrast is used to measure only part of a share or portfolio’s risk, namely the part that cannot be reduced by diversification, that is the systematic or market risk of an individual share or portfolio of shares. Systematic risk can be further subdivided into business risk and financial risk. Business risk arises from the nature of the firm’s business environment and the particular characteristics of the type of business or industry in which it operates. For example the competitive structure of the industry, its sensitivity to changes in macroeconomic variables such as interest rates and inflation and the stability of industrial relations all combine to determine a firm’s business risk.
The level of business risk in some industries, for example catering and construction, is higher than in others and is a variable which lies largely outside management’s control. Financial risk in contrast represents the risk which arises from a firm’s level of gearing or leverage and is a variable which is directly under management’s control. Basically the more debt a firm has, the greater the level of financial risk (that is, the risk of the firm not being able to meet its financial obligations). In practice, the market portfolio would be impossible to achieve, so to operationalise the CAPM theory, a sufficiently large stock market index such as the Financial Times Stock Exchange (FTSE) 100 Share Index (i.e. the ‘Footsie’ 100 index) or the FTSE All-Share index is substituted for the market portfolio.
3. There are three forms of market efficiency: weak, semi-strong and strong.
Strong form efficiency goes a stage further than the semi-strong form and asserts that current market prices will immediately and fully reflect all relevant information, whether publicly or privately held: by definition this includes the inside information possessed by a firm’s directors and managers.
There is less evidence to support this form of efficiency than the other two. Financial market efficiency has important implications for the investment and financing decisions, not only of individual investors but also of the firm. If, generally speaking, financial markets are considered weak to semi-strong form efficient then a number of important implications follow. Under the efficient market conditions, it is impossible for any investor to consistently outperform the market. Consistently is the key term here. A security’s market price at any point in time is a true reflection of its intrinsic value (that is its fair value as perceived by the investor), thus in an efficient market intrinsic value and market value are the same—in other words the price is always right! In an efficient market it is not possible to accurately predict security price movements.
As security prices already incorporate all past and publicly available information, that is, there is semi-strong from efficiency, then prices will only be affected by new, currently unknown information at some stage in the future—if the information was known now it would already be reflected in the security’s current price, it would not be ‘news’. If future events are uncertain, random and unpredictable then new information will arrive in the markets in an uncertain, random and unpredictable manner. The corollary of this is that if information about future events is uncertain then so too are future security prices. The best estimate of a security’s value is the consensus view of a competitive, efficient market Thus individual investors performing their own security analysis and trying to beat the market are simply wasting their time. This does not imply, however, that it is similarly a waste of time for investment firms to engage in security analysis.
4. The following theorems were originally developed by Burton G. Malkiel.
- THEOREM 1: Bond prices are positioned inversely to interest rate changes. When y%uF0AD %uF0DE ………………. When y%uF0AF %uF0DE ……………….
- THEOREM 2: The longer the time to maturity of the bond, the more perceptive it is to changes in interest rates.
- THEOREM 3: The price alterations resulting from equal absolute rises in YTM are not symmetrical. For any given maturity, a x% fall in YTM causes a price increase that is larger than the price loss resulting from an equal x% increase in YTM.
- THEOREM 4: The lower a bond’s coupon, the more perceptive its price will be to the market alterations in interest rates.
5a. Where should one begin in order to make an investment decision?
Consider that the ultimate in simplicity comes with the additional virtue of low cost. The simplest of all approaches is to invest solely in a single balanced market index fund—just one fund. And it works. Such a fund offers a broadly diversified middle-of-the-road investment program for a typical conservative investor who is investing about 65 percent of assets in stocks and 35 percent in bonds. This portfolio is entirely “indexed”—that is, its stocks and bonds are not actively managed, but simply represent a broad cross-section of the entire U.S. stock market and bond market. Over the past half-century, such a fund would have captured 98 percent of the rate of return of the combined stock and bond markets. Investing doesn't get much better than that.
5b. Let us illustrate the point of decision making regarding investing in an index fund.
I'll compare the cumulative returns of the average balanced fund with a hypothetical no-load balanced index fund weighted 35 percent by the Lehman High-Grade Corporate Bond Index and 65 percent by the Standard & Poor's 500 Stock Index (rebalanced annually), with the annual return reduced by estimated costs of 0.2 percent. We'll take a half-century retrospective, in order to gain a broad view from the lessons of history.
Note these three key observations:
- At the end of the half-century, the initial $10,000 investment would have grown to $1,615,000 for the passively managed index fund, versus $1,080,000 for the actively managed traditional fund—a compound annual return of 10.7 percent, compared to 9.8 percent for the average balanced fund (and 10.9 percent for the composite index itself). When time and compounding join forces, this seemingly modest 0.9 percent advantage in annual return for the index fund over the average actively managed fund has created a profound difference in accumulated wealth—fully $535,000 (Carhart 57-72).
- Little things mean a lot. The superiority of the index fund is not a matter of magic. The heavy costs of managed funds accounted for precisely 100 percent of the differential in rate of return. The average balanced fund incurred annual operating expenses of 0.9 percent, on average, during the period, and perhaps another 0.2 percent in portfolio turnover costs—a total handicap of 1.1 percent. The index fund cost was 0.2 percent, an advantage of 0.9 percent. That cost advantage is what made the difference (Carhart 57-72).
- While managed funds earned annual returns equal to 90 percent of the market returns for a 65/35 stock/bond portfolio, at the end of 50 years the final value was just 61 percent of the value of the market portfolio. For the balanced index fund, however, the final value was 92 percent of that of the market portfolio, more than half again as large as the managed funds (Lowenstein C1-C2). Fifty years, to be sure, is a long time. The past 15 years may be more relevant for appraising today's fund industry, so let's look at the 35 balanced funds that have survived that period. As it turns out, you would have been wise not to waste your energy trying to find the best manager. Only two funds outpaced the low-cost index fund for the full period (Lowenstein C1-C2).
During the past 15 years—including most of the bull market, with stock returns near historic highs—the average return of the actively managed balanced funds was 12.8 percent per year, compared with 14.7 percent for the balanced index fund, without a noticeable difference in risk. That 1.9 percent deficit may not matter to investors when they still earn 12.8 percent net, but when stock returns recede to more normal levels—as they are apt to—the deficit's significance will be more apparent (Lowenstein C1-C2).
5c. What I have described here is the very essence of simplicity: owning the entire U.S. stock market (and, for a balanced index fund, the entire U.S. bond market as well); making no effort to select the best manager; holding the asset allocation constant and making no attempt at market timing; keeping transaction activity low (and minimizing taxes as well); and eliminating the excessive costs of investing that characterize managed mutual funds. And it worked. Even if future outcomes of this approach are less successful, it's hard to imagine that they could provide markedly inferior wealth accumulation relative to comparable managed funds. The success of the index fund reaffirms a basic piece of investment wisdom: When all else fails, fall back on simplicity.
6 a. In the past 25 years, we have come to frame the simple logic of diversification in terms of a rigorous statistical model developed by finance academics: Modern Portfolio Theory. Investors almost universally accept this theory, which is based on developing investment portfolios that seek returns that optimize the investor's willingness to assume risk. Risk, in turn, is defined in terms of short-term fluctuations in expected value. In its most comprehensive form, modern portfolio theory dictates that portfolio composition should include all liquid asset classes—not only U.S. stocks, bonds, and cash reserves, but international investments, short positions, foreign exchange, and various curios (gold, for example) from the financial marketplace. For simplicity's sake, we omit cash reserves such as money market funds from the equation. Because they tend to deliver very modest returns, such reserves should be considered as savings for short-term and emergency needs, not as investment for long-term capital accumulation. For investors, short-term bonds are a superior alternative to money market funds. Short-term bonds are relatively insensitive to interest rate fluctuations; long-term bonds are hugely sensitive. The general diversification guidelines are simple: as a crude starting point, two-thirds in stocks, one-third in bonds.
6b. Balance optimizes returns from the stock market in order to reach investment goals such as the accumulation of assets for retirement, but it holds the risk of loss to tolerable levels by ownership of some bonds, too. Despite (or perhaps because of) the long bull market in stocks that has made balanced investing seem old-fashioned and stodgy to some advisers, I continue to advocate a balanced policy today—with more enthusiasm than ever. The general diversification guidelines also respect what many call the four dimensions of investing: (Carhart 57-72) return, (Lowenstein C1-C2) risk, (3) cost, and (4) time. When you select your portfolio's long-term allocation to stocks and bonds, you must make a decision about the real returns you can expect to earn and the risks to which your portfolio will be exposed. You must also consider the costs of investing that you will incur. Costs will tend to reduce your return and/or increase the risks you must take.
7. The second key characteristic of the APT model is that it is a multi-factor model. This is in sharp contrast to the CAPM which is a single factor model, relying as it does solely on the market portfolio to determine security returns. In APT the market portfolio has no special role. The APT model asserts that there are other variables at play which determine a security’s return other than the market portfolio. The APT model prefers to incorporate multiple risk factors, each with its individual beta, to explain security returns. The APT model essentially states that the expected rate of return on a security in equilibrium is equal to the risk-free rate plus multiple risk premiums, (instead of the single market risk premium as postulated by the CAPM). In other words, each factor in the APT model has its own risk premium, which is determined by multiplying the security’s sensitivity to unanticipated changes in a range of economic factors by the market risk premium for each factor. It does not matter how many factors there are, as long as they are less than the number of securities. The APT model, for a zero arbitrage economy, can be expressed mathematically as: ERj =Rf +βj1 RP1 +βj2 RP2 +βj3 RP3 +…+βji RPn where, ERj = expected return on security j Rf = risk-free rate βji = beta coefficient indicating the sensitivity of security j’s returns to unexpected changes in factor i RPi = market risk premium for factor i There is no general consensus among academics and practitioners as to how many factors should be included, nor even as to their identities.
Roll and Ross (1980, 1984) have identified four factors for the model which are likely to determine security returns. They are unanticipated changes in: industrial production, inflation, default risk premium on bonds, and the term structure of interest rates. The reason for using unanticipated changes in factors is that any anticipated changes will have already been absorbed by the market into expected rates of return on securities.
The APT model is considered superior to the CAPM as it incorporates multiple economic factors to explain security returns. The CAPM can be viewed as a special case of the APT. The assumptions of the APT model are also less restrictive than those of CAPM. APT does not, for example, assume a single time period horizon or that investment decisions are made within a mean-variance context—that is, unlike CAPM it does not assume that investors consider their portfolios in terms of required returns and variance. However, the APT model is much more complex than CAPM and is theoretically unclear about the nature and number of relevant risk factors.
Moreover it is very difficult to establish each factor’s risk premiums and to measure their sensitivity coefficients. This makes the model almost impossible to put into practice. To date, the APT model is still in its relative infancy. The empirical work which has so far been done does not provide any conclusive results on the efficacy of the model. In conclusion, both the APT and CAPM do offer us alternative conceptual frameworks for trying to understand the connections between risk and return and thus the task of valuing securities. However, academics and researchers are still a long way from developing a universal asset pricing model and the theory of asset pricing remains in a confused state.