The Major Formulas and Terms For Portfolio Theory, CAPM. 1. There will be no successful investment managers who can consistently beat the market. Portfolio Management refers to the process of selection of a bundle of securities with an .. CAPM return need to be calculated by formula, Rf + β (Rm – Rf). Portfolio Management refers to the process of selection of a bundle of Step 1: Calculate HPR for different years, if it is not directly given in the Question.

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Management Formulas: Mathematical Trading Methods for the .. Chapter 11 examines what portfolio managers have (not) been doing. (b) Calculate the simple weighted standard deviation of the portfolio and comment (a) Discuss the key characteristics of 'passive' fund management and . Risk-Return Calculations of portfolios with more than two securities “Portfolio analysis considers the determination of future risk and return in holding various .. securities is the first step in portfolio management and is called portfolio analysis.

Updated Jun 22, Expected Return vs. Standard Deviation: An Overview Expected return and standard deviation are two statistical measures that can be used to analyze a portfolio. The expected return of a portfolio is the anticipated amount of returns that a portfolio may generate, whereas the standard deviation of a portfolio measures the amount that the returns deviate from its mean. Expected Return Expected return measures the mean, or expected value, of the probability distribution of investment returns. The expected return of a portfolio is calculated by multiplying the weight of each asset by its expected return and adding the values for each investment. Therefore, the expected return of the portfolio is 7.

A set of efficient portfolios can be generated by using the above process of combining various securities whose combined risk is lowest for a given level of return for the same amount of investment, that the investor is capable of.

The theory of Markowitz, as stated above is based on a number of assumptions. Assumptions of Markowitz Theory: The Portfolio Theory of Markowitz is based on the following assumptions: 1 Investors are rational and behave in a manner as to maximise their utility with a given level of income or money.

Diversification of securities is one method by which the above objectives can be secured.

The unsystematic and company related risk can be reduced by diversification into various securities and assets whose variability is different and offsetting or put in different words which are negatively correlated or not correlated at all. Diversification of Markowitz Theory: Markowitz postulated that diversification should not only aim at reducing the risk of a security by reducing its variability or standard deviation, but by reducing the covariance or interactive risk of two or more securities in a portfolio.

As by combination of different securities, it is theoretically possible to have a range of risk varying from zero to infinity. Markowitz theory of portfolio diversification attaches importance to standard deviation, to reduce it to zero, if possible, covariance to have as much as possible negative interactive effect among the securities within the portfolio and coefficient of correlation to have — 1 negative so that the overall risk of the portfolio as a whole is nil or negligible.

The standard deviation of the portfolio determines the deviation of the returns and correlation coefficient of the proportion of securities in the portfolio, invested. Parameters of Markowitz Diversification: Based on his research, Markowitz has set out guidelines for diversification on the basis of the attitude of investors towards risk and return and on a proper quantification of risk.

The investments have different types of risk characteristics, some called systematic and market related risks and the other called unsystematic or company related risks.

Markowitz diversification involves a proper number of securities, not too few or not too many which have no correlation or negative correlation. The proper choice of companies, securities, or assets whose return are not correlated and whose risks are mutually offsetting to reduce the overall risk.

For building up the efficient set of portfolio, as laid down by Markowitz, we need to look into these important parameters: 1 Expected return. In general the higher the expected return, the lower is the standard deviation or variance and lower is the correlation the better will be the security for investor choice.

Whatever is the risk of the individual securities in isolation, the total risk of the portfolio of all securities may be lower, if the covariance of their returns is negative or negligible.

Criteria of Dominance: Dominance refers to the superiority of one portfolio over the other. A set can dominate over the other, if with the same return, the risk is lower or with the same risk, the return is higher. Dominance principle involves the tradeoff between risk and return.

The above concepts are used in the calculation of expected returns, mean standard deviation as a measure of risk and covariance as a measure of inter-relations of one security return with another.

Measurement of Risk: Risk is discussed here in terms of a portfolio of assets. Any investment risk is the variability of return on a stock, assets or a portfolio.

It is measured by standard deviation of the return over the Mean for a number of observations. Portfolio Risk: When two or more securities or assets are combined in a portfolio, their covariance or interactive risk is to be considered. Thus, if the returns on two assets move together, their covariance is positive and the risk is more on such portfolios.

If on the other hand, the returns move independently or in opposite directions, the covariance is negative and the risk in total will be lower. The coefficient of correlation is another measure designed to indicate the similarity or dissimilarity in the behaviour of two variables. Indeed, risk in financial investments is not variance in itself, rather it is the probability of losing: it is asymmetric in nature.

Barclays Wealth have published some research on asset allocation with non-normal returns which shows that investors with very low risk tolerances should hold more cash than CAPM suggests. A different possibility is that active and potential shareholders' expectations are biased, causing market prices to be informationally inefficient. This possibility is studied in the field of behavioral finance , which uses psychological assumptions to provide alternatives to the CAPM such as the overconfidence-based asset pricing model of Kent Daniel, David Hirshleifer , and Avanidhar Subrahmanyam Empirical studies show that low beta stocks may offer higher returns than the model would predict.

Either that fact is itself rational which saves the efficient-market hypothesis but makes CAPM wrong , or it is irrational which saves CAPM, but makes the EMH wrong — indeed, this possibility makes volatility arbitrage a strategy for reliably beating the market.

It does not allow for active and potential shareholders who will accept lower returns for higher risk. Casino gamblers pay to take on more risk, and it is possible that some stock traders will pay for risk as well.

This assumes no preference between markets and assets for individual active and potential shareholders, and that active and potential shareholders choose assets solely as a function of their risk-return profile. It also assumes that all assets are infinitely divisible as to the amount which may be held or transacted. In practice, such a market portfolio is unobservable and people usually substitute a stock index as a proxy for the true market portfolio.

Unfortunately, it has been shown that this substitution is not innocuous and can lead to false inferences as to the validity of the CAPM, and it has been said that due to the inobservability of the true market portfolio, the CAPM might not be empirically testable.

This was presented in greater depth in a paper by Richard Roll in , and is generally referred to as Roll's critique. This is in sharp contradiction with portfolios that are held by individual shareholders: humans tend to have fragmented portfolios or, rather, multiple portfolios: for each goal one portfolio — see behavioral portfolio theory [20] and Maslowian portfolio theory.