代写FINC3017 INVESTMENTS AND PORTFOLIO MANAGEMENT

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–FINC3017 INVESTMENTS AND PORTFOLIO MANAGEMENT

–DR ANDREW AINSWORTH

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–Learning Objectives

–How are returns generated?

–We can assume a single factor structure

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–How does this help us in terms of portfolio optimisation?

–Reduces the number of inputs required for mean-variance optimisation

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–One factor drives the returns of securities

–We can obtain estimates from regression analysis

–Provides some economic intuition to portfolio construction

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–What are the benefits and limitations of mean variance optimisation?

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–Reading

–BKM Ch. 8

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–Kritzman, M. (2011) “The graceful aging of mean-variance optimization”, Journal of Portfolio Management, Vol. 37 Issue 2, pp. 3-5. http://opac.library.usyd.edu.au:80/record=b4152264~S4

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–Michaud, R.O. (1989) “The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?”, Financial Analysts Journal, Jan-Feb, pp. 31-42. http://opac.library.usyd.edu.au:80/record=b4152266~S4

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–The Single Index Model (SIM)

–Markowitz framework requires a significant number of inputs when dealing with a large number of securities

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–We can simplify the portfolio optimisation task by assuming that the risk of an individual security can be decomposed into a firm specific component and a market wide component

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–Sharpe (1963) overcame this problem using the Single Index Model (SIM)

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–The SIM uses this assumption to specify a particular form for security returns and simplify the portfolio selection problem

›This reduces the number of required inputs

–代写FINC3017 INVESTMENTS AND PORTFOLIO MANAGEMENT

–SIM

–Returns can easily be expressed as an expected component and an unanticipated component in the following way:

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–where ui has a mean of zero and standard deviation si

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–Individual returns are generally correlated with each other

–Common set of factors drive returns (e.g. common response to market changes)

–Assume all stock returns are related to a single influence (market return)

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–Under the assumption of a single factor, security returns could be written as:

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–The macroeconomic factor (m) measures unanticipated macroeconomic surprises and therefore has a mean of 0 and a standard deviation of sm

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–SIM

–SIM describes an asset return as made up of a constant and a sensitivity to a factor

–This factor is often the ‘market’ index (e.g. ASX200, S&P500, FTSE100)

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–Where

–Rit is the return on asset i in period t

–Rmt is the return on the factor in period t

–ai is the constant component of asset i’s return

–bi is the sensitivity of asset i’s return with the factor

–eit is residual component of asset i’s return that is not explained by the factor

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–SIM

–The residual (eit) is assumed to be uncorrelated across assets and time, and is also uncorrelated to the factor return (Rmt)

–The residual is assumed to have a mean of zero and a variance of

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–Sharpe assumes that the returns to the factor (Rmt) are generated as:

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–Where A is a constant and c is a random residual

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–This implies that the expected return on the factor is:

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–The standard deviation of the factor is simply:

–SIM

–The expected return and variance for asset i are then:

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–代写FINC3017 INVESTMENTS AND PORTFOLIO MANAGEMENT

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–The covariance between asset i and j is

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–The variance of the portfolio is then

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–SIM

–Let’s assume the factor is the return on the ASX300 index (Rm)

–It is also common to work in ‘excess return’ form and deduct the risk-free rate from the both the asset’s returns and the market’s return:

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–If the excess return on the market is zero, then ai represents the expected excess return on the stock

–The sensitivity of the securities return is given by bi (the larger bi is, the greater the swings in a stocks return when the market moves)

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–Given that E(ei) = 0, we can similarly express expected returns as

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–This is the expected return-beta relationship

–SIM and Diversification

–The SIM also provides intuition about the benefits of diversification

–Let’s assume that portfolios are equally weighted (xi =1/N)

–Alpha, beta and residual risk are therefore the averages:

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–SIM and Diversification

–The return on a portfolio under a SIM is given by:

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–SIM and Diversification

–Consider now the variance of the returns on this portfolio:

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–Since all the firm specific variance are assumed to be independent, we have that

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–Since the average variance is independent of N, as N grows (more firms are added) the portfolio’s idiosyncratic variance converges to zero

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–As an investor increases the number of assets in their portfolio, the proportion of total risk that is systematic risk will increase and in the limit, their portfolio variance approaches :

–SIM and Diversification

–Estimation

–Now that we have developed our model, the question remains as to how it might be estimated?

–代写FINC3017 INVESTMENTS AND PORTFOLIO MANAGEMENT

–The simplest (and best) way is to perform the regression model described earlier

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–We will consider 60 monthly returns from August 2011 to July 2016 on Commonwealth Bank (CBA), Ramsay Health Care (RHC) and Woodside (WPL)

–The ASX200 is the single factor

–The 90-day Bank-Accepted Bill rate is the risk free rate

–We are working in excess return form

–Monthly excess returns

–Estimation: CBA

–Estimation: RHC

–Estimation: WPL

–Estimating the SIM

–Beta estimates can be supplied through commercial vendors or calculated directly

–Require returns on the individual security

–Require returns on a market index such as the S&P/ASX 200 accumulation index

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–Beta can be estimated using the following regression:

–Beta estimates are imprecise:

–They vary according to data used for estimation

–Thin trading creates bias

–They vary over time for same firm

–Measurement error in beta

–If a share is traded infrequently (thinly) then beta estimates using the above approach can lead to a bias in the measurement of beta

–First order serial correlation between today and yesterday

–Consider a case where the last trade in small and illiquid security, ARR happens at 1:20pm on a given day

–If there is some news announcement between 1:20pm and the market close at 4:10pm that affects the entire market then the use of this return in a regression to estimate beta will be biased

–When ARR next trades (e.g. the following day), its share price will adjust to this news

–However, the market return the following day will be unrelated to the previous days news (on average)

–We can correct for this bias using a Dimson (1979) adjustment

–Measurement error in beta

–Dimson (1979) adjustment :

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–Where

–Ri,t is excess return on stock i at time t

–Rm,t is excess return on the market portfolio at time t

–ei,t is the residual from the regression

–k is the number of lagged market returns

–j is the number of leading market returns

–The stock’s beta is

–Alpha and Security Analysis

–The Treynor-Black Model

–Use macroeconomic analysis to estimate risk premium and risk of market index

–Use statistical analysis to estimate the beta coefficients of all securities and their residual variances, σ2(ei)

–Establish the expected return of each security absent any contribution from security analysis

–Use security analysis to develop private forecasts of the expected returns for each security

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–You can invest some portion in the market portfolio and some portion in an ‘active’ portfolio

–If you only care about diversification then you hold the market portfolio

–If you find alpha through security analysis you will not hold the market

–Mod代写FINC3017 INVESTMENTS AND PORTFOLIO MANAGEMENT