Notes on portfolio management and security analysis PDF

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Class lecturer: Jonathan Fletcher...

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Notes of Portfolio Management and Security Analysis Introduction Types of Financial Securities Direct v Indirect investments Direct – when buy the financial assets directly. Indirect – when hold financial assets indirectly through a managed fund. Direct Investments: 1) Money market instruments – short-term debt securities with maturities less than one year. 2) Capital market instruments – common stock (equity), and debt securities with a maturity longer than one year. 3) Derivative instruments – securities whose payoff depends upon the price of another asset. For example, an option is the right but not the obligation to buy or sell an asset at an agreed price at some future date. Derivative securities will be considered in your third year Finance classes. Money market securities 1. Treasury Bills These are short-term zero-coupon bonds issued by the government which pays the face value of the bond at maturity. The bonds are issued at a discount to the face value and so the investor knows the return of the T. Bill when buying the bill. In nominal terms, T. Bills are risk-free. In the U.K., bills are issued at 1-month, 3-months, and 6-months maturities and sold in minimum denomination of £500,000 (U.K. Debt Management Office). 2. Certificates of deposit, commercial paper, and floating rate notes. Capital market securities

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1. Stocks – ordinary shares issued by the company. Legal owners of the company. Payoffs are periodic dividends and future sale of share (price at some future date). Trade on the London Stock Exchange or the Alternative Investment Market. 2. Bonds – these are debt securities issued by companies or governments. Usually have a fixed life. Pay regular coupon payments and the face value of the bond at the end of the life of the bond. Will consider bonds more fully later in the class. Indirect investments: 1. Retail funds These are investment funds that can be bought by the general public. Known as mutual funds.

Main types are open-end funds (Unit trusts and Open-Ended

Investment Companies (OEIC), closed-end funds (investment trusts), and exchange traded funds. 2. Pension funds 3. Insurance companies 4. Hedge funds 5. Private equity funds 6. Sovereign wealth funds Will consider some of the different types of funds later in the class. Benchmarks and Market Indexes Benchmarks of major asset classes and investment styles are important for a number of reasons. First, it provides information on well a given asset class or style has performed over some historical period. Second, benchmarks are used to evaluate the

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performance of fund managers. The benchmark is used as a passive alternative trading strategy that the fund manager could have followed. Third, benchmarks are used in the developing of index funds and Exchange Traded Funds. Fourth, the benchmarks are used in asset allocation decisions. Stock market indexes: Most stock markets have local stock market indexes. In the U.K., the main ones are the FT100 and FT All Share index. These are value weighted indexes of the largest stocks on the London Stock Exchange. The weights depend upon the market values of the stocks. Some indexes like the Japan Nikkei 225 index uses equal weights. The Dow Jones Industrial Average is a price-weighted index. Indexes are also provided by organizations like MSCI, FTSE, S&P, Russell Investments, Thomson Financial Datastream. Provide both local indexes, regional, and global indexes. Also construct industry indexes, style indexes. Advantage is that use the same methodology across all markets. MSCI use market value weights. In emerging markets, S&P/IFC produce investable indexes that represent the market that is actually available to international investors. Global index providers differ in their coverage of each market and the weights that are used. In some markets, free float market cap weights are used. The free float is the proportion of the market value weights that are available to international investors. International investors do not always have access to the full market value due to cross holdings, government ownership, restrictions on foreign holdings. Data providers also provide bond indexes for local and global bond markets. Benchmarks have also been created for other asset classes e,g gold or commodities. These indexes are easily accessible through databases like Thompson Financial Datastream and Bloomberg

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An Introduction to Statistics The return (Rt+1) on any asset over a single time period is given by: Rt+1 = [(Pt+1 + Dt+1)/Pt] – 1 where Pt+1 is the price of the asset at time t+1, Pt is the price of the asset at time t, and Dt+1 is the dividend or income from asset (if any at time t+1). Can also write as: Rt+1 = [(Pt+1 – Pt + Dt+1)/Pt] The return on the asset comes in the form of a capital gain/loss (P t+1 – Pt) and income if any (Dt+1). The

example.xlsx

file

contains

data

on

the

monthly

returns

on

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volatility/momentum portfolios (Columns numbered 1-15) between July 1983 and December 2015. The worksheet also contains the return on the one-month U.K. Treasury Bill (Rf) and the excess returns on the market index (Market) and two zerocost portfolios that capture the size (SMB) and value (HML) effects in U.K. stock returns. We will be using Matlab through this class. The portfolio optimization handbook will give you an introduction to Matlab. To issue a command, you type in the relevant command at the command prompt. The command prompt in Matlab is given by: >> To import data into Matlab, we can either use the approach in section 2.3 of the workbook or a related approach where we just specify the relevant part of the worksheet. input_file='example.xlsx'; input_sheet='Sheet1';

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mkt=xlsread(input_file,input_sheet,'s2:s391'); We will focus on how to estimate the mean and standard deviation of the excess market returns. Section 3 of the portfolio optimization workbook shows how to use Matlab to get descriptive statistics and to plot graphs. For the average excess market return, use the command mean: 100*mean(mkt)

% calculates the mean in % terms

0.4141 If multiply by 12, get an annualized mean excess return. 12*mean(mkt)*100 4.9695 For the standard deviation use the command std: std(mkt)*100 4.2322 To get the annualized volatility, multiply by the √12 sqrt(12)*std(mkt)*100 14.6607 The excess market returns during the sample period of July 1983 and December 2015 has an annualized average of 4.96% and volatility of 14.66%. The average excess market returns is known as the historical equity premium. An important issue in many practical applications is whether the average excess market returns are significantly positive or do stocks significantly outperform risk-free bonds? We can examine this issue by conducting a statistical test of the hypothesis that the average excess market return is equal to zero.

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Statistical tools provide estimates of relevant parameters and the sampling distribution of the parameters. The sampling distribution tells us how precise the estimate is measured. The uncertainty of the estimate is captured by the standard deviation of the sampling distribution or it’s standard error. In the case of the average excess returns, we want to know what the standard error of the average excess market returns is. Under standard statistical assumptions, the excess market returns are independently and identically distributed (iid), the standard error of the average excess market returns is given by: SE(rm) = σ(rmt+1)/√T The standard error tells us how volatile the estimate is and captures sampling variation. We want to test whether rm= 0. This is known as the null hypothesis (H0). The alternative hypothesis (Ha) is usually that rm ≠ 0. Where the alternative hypothesis allows for either positive or negative values, this is known as a two-tail test. Where the alternative hypothesis is rm > 0 or rm < 0, this is known as a one-tail test. We use a statistical test to examine the null hypothesis. The test allows us to judge whether the average excess market returns are different from zero due to sampling variation (accept null) or due to a real difference (reject null). We can test the null hypothesis that average excess returns=0 using the standard tstatistic t-statistic = (Estimate - Value of estimate under the null)/Std error of estimate

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In our case, since the value of estimate under the null equals zero, the t-statistic is simply the average excess returns divided by the standard error of average excess returns. A large absolute value of the t-statistic (depending upon the specified significance level) leads to a rejection of the null hypothesis. To decide whether to accept or reject the null hypothesis, we can compare the actual tstatistic to the critical values of the t-statistic from the t-distribution. When T is large, the t-distribution converges to a standard normal distribution. As a rough rule of thumb for large T: If |t| is > 1.96, then we can reject the null hypothesis at the 5% significance level If |t| is > 1.64, then we can reject the null hypothesis at the 10% significance level An alternative approach is to use the p value of the t-statistic. The p value is the probability of observing the t-statistic. We reject a given null hypothesis if the p value of the t-statistic is below a specified significance level (1%, 5%, 10%). Assume a 5% significance level. If the p value < 0.05, and the t-statistic is positive, we reject the null hypothesis and the coefficient is significantly positive. If the p value < 0.05, and the t-statistic is negative, we reject the null hypothesis and the coefficient is significantly negative. A significant positive average excess returns implies the market return has a significantly higher average returns than risk-free bonds. A significant negative average excess returns implies that the market returns have a significantly lower average returns than risk-free bonds.

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We can also use the standard error of the average excess returns to compute confidence intervals of the average excess market returns. The 95% confidence interval of the average excess market return (rm) is rm – 1.96*SE(rm) 0 (positive market risk premium) R2 = 1, market betas explain all of the cross-sectional variation in the average excess returns. The null hypotheses that we test here are: γ0 = 0 and γ1 = 0 If the CAPM is true, we want to accept γ0 = 0, and reject γ1 = 0 in favour of a significant positive γ1. The R2 should also be close to 1. We can also get a visual fit of the CAPM by plotting average excess returns (y-axis) against betas (x-axis). If the CAPM is well specified, all of the points should plot on a upward sloping straight line. disp('Betas'); 54

disp(reshape(beta',3,5)'); Betas 0.9523

0.9273

0.8508

1.2260

1.1126

1.0206

1.4679

1.2940

1.1670

1.4922

1.3905

1.3038

1.5280

1.4363

1.4124

There are patterns in the spread of the betas. The Winners portfolios have lower market betas than Losers portfolios. The low volatility portfolios have lower market betas than high volatility portfolios. This is the opposite to what we would expect from the CAPM. The low volatility and winners portfolios should have higher market betas to explain the higher average excess returns of these portfolios. figure(1) xlabel('Beta') ylabel('E(r)') title('E(r) v Beta') hold on; scatter(beta,u) hold off;

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E( r )vBe t a 0 . 0 1 0 . 0 0 8 0 . 0 0 6 0 . 0 0 4

E( r )

0 . 0 0 2 0 0 . 0 0 2 0 . 0 0 4 0 . 0 0 6 0 . 0 0 8 0 . 0 1 0 . 8

0 . 9

1

1 . 1

1 . 2 B e t a

1 . 3

1 . 4

1 . 5

1 . 6

Graph confirms the poor performance of the CAPM. The high beta portfolios have the lowest mean excess returns and the low beta portfolios have the highest mean excess returns. Use the command: LinearModel.fit(beta,u) Estimated Coefficients: Estimate SE tStat pValue (Intercept) 0.023912 0.0070863 3.3744 0.0049819 x1 -0.017323 0.0056355 -3.0739 0.0088824 Number of observations: 15, Error degrees of freedom: 13 Root Mean Squared Error: 0.00471 R-squared: 0.421, Adjusted R-Squared 0.376 F-statistic vs. constant model: 9.45, p-value = 0.00888 The null hypothesis of γ0 = 0 and γ1 = 0 is rejected with tiny p values. The γ0 is significantly positive, which shows that the intercept is a lot higher than Rf. The γ 1 coefficient is significantly negative at -1.73%. This is a huge negative market risk

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premium and confirms the graphical results. The CAPM is a disaster here with this set of test assets. The R2 is 42.1% and is far away from 1. Limitations of the CAPM: 1. Can we identify the market portfolio? (Roll(1977)). Roll(1977) argues that

the CAPM is not testable since M cannot be observed.

Known as the Roll Critique Most empirical studies and practical applications use a stock market index as a proxy for the market portfolio. CAPM makes no predictions about market proxies. 2. Poor empirical performance The standard CAPM using a stock market index as a proxy for the market portfolio tends to perform poorly in explaining cross-sectional stock returns.

Fama and

French(1992) find no relation between average returns and betas in U.S. stock returns. Stock characteristics help to explain average returns beyond the market betas. Fama and French find that size and book-to-market ratios both help explain cross-sectional average returns. A negative relation between size and average returns and a positive relation between BM ratio and average returns. See the review paper by Fama and French(2004) for empirical evidence on the CAPM. 3. Estimating Betas and Market Risk premiums for Practical Applications Using the CAPM in practical applications is difficult as the true betas and market risk premiums are unknown and must be estimated. We can estimate betas from historical regressions and the market risk premium from the historical average excess market returns. However only valid if the risk premiums and betas are constant over time. Likely to be time-varying, which complicates the estimation issues.

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We will consider evidence of the CAPM in more detail when we look at multifactor models. Multifactor (Multi-Index) Models Arbitrage Pricing Theory (APT) Ross(1976) developed an alternative approach to the CAPM, which allows for more than one risk factor. Known as the Arbitrage Pricing Theory (APT). The APT makes no strong assumptions about investor behaviour. The key assumption is that all investors believe that asset returns are driven by a linear K-index (factor) statistical model: Rit+1 = ai + bi1I1t+1 + bi2I2t+1 + ….. + biKIKt+1 + eit+1 = ai + k=1KbikIk + eit+1 where Rit+1 is the return on asset i at time t+1, I kt+1is the unanticipated value of the kth factor at time t+1 (E(Ikt+1)=0) for k=1…,K, ai is the expected return of asset i if all the indexes have a zero value, bik is the beta of asset i relative to factor K for k=1,…,K, eit+1 is a random error term, and K is the number of factors in the model. The factor model splits the unanticipated stock return (Rit+1 – ai) into a part that is due to K common factors and a residual term (eit+1). The K common factors explain the covariance matrix of the asset returns such that for any two securities i and j E(eit+1,ejt+1) ≈ 0 i.e. there should be no correlation between the residuals of any two securities. Ross shows that under a linear statistical model, if no arbitrage holds in financial markets, then there must be a linear relation between expected returns and the K factor betas (bi1 to bik). The argument really stems from the Law of One Price (LOP). The LOP states that any two assets with identical payoffs must sell for the same price otherwise investors could make an instantaneous profit by short selling the more

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expensive asset and buying the cheaper asset. This strategy involves no wealth and has zero risk. In competitive markets, investors will exploit violations of the LOP. If eit+1 = 0, then the return on asset i can be perfectly replicated by the return of a portfolio of the K factors. Under the LOP, these two payoffs must have the same price and so we can price the asset relative to the K factors. This results in the APT risk-return equation: E(Ri) = Rf + λ1bi1 + λ2bi2 + …. + λKbik E(Ri) - Rf = E(ri) = k=1Kbikλk where bik is the beta of asset i relative to factor k (a regression slope coefficient), and λk is the risk premium of factor k where λk = E(Rk) – Rf. The equation above is the APT equivalent to the SML. It is a multifactor model as systematic risk is multi-dimensional. The APT is a general model. However the theory does not tell what the K common factors are and how many are important. It also tells us nothing about the size or signs of the λ’s. The APT makes similar testable predictions to the CAPM. Only differences in systematic risk (K betas) explain the cross-sectional differences in expected returns and stock characteristics should have no impact on expected returns after controlling for systematic risk. Estimating and Testing the APT To evaluate the APT, we require to identify the K factors I kt+1, the factor betas bik, and the factor risk premiums λk. A number of different approaches have been adopted in the literature. 1) Estimate the factors Ikt+1 and betas bik jointly. This approach uses statistical tools such as factor analysis or principal components analysis to identify a small number of factors (statistically) that explains the

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covariance matrix of asset returns. The factor risk premiums can then be estimated from a cross-sectional regression of average returns on the K factor betas. Roll and Ross(1980) are an early example of this approach. Main downside is that the factors lack economic meaning. The main alternative empirical approach is to specify the K common factors. EGBB suggest one approach is to use stock characteristics as the K common factors. The characteristics would be the corresponding bik’s. We could then estimate the factor premiums from cross-sectional regressions. Downside of this approach is that what is the economic theory of the stock characteristics and why should they be treated as common factors. As a result, most studies when using the APT either specify the factors as: 1. Macroeconomic factors – where the factors are selected on the basis of economic theory.

The classic study is Chen, Roll and Ross(1986).

The factors include

unanticipated changes in inflation, term structure of interest rates, default spread, and industrial production. The model can be evaluated using the same two-pass approach as we did for the CAPM. Chen et al and Burmeister and McElroy(1988) find that macroeconomic factors often have significant factor risk premiums.

Cooper,

Mitrache and Priestley(2016) are a recent application of a global factor model based on global macroeconomic factors. 2. Portfolio factors – where the factors are formed on the basis of stock characteristics that are known to explain cross-sectional average stock returns. These factors usually arise out of tests of the CAPM/market efficiency. These models are also known as empirical factor models.

In the Fama and

French(1993) model, they add a size factor (SMB) and a value/growth (HML) factor to the excess market returns to create a three-factor model.

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SMB is a zero-cost portfolio that captures the difference in returns between small companies and large companies, and HML is a zero-cost portfolio that captures the difference between value companies and growth companies. Numerous linear factor models have been proposed within this group which essentially ...