Modern Portfolio Theory Adaptations ( Pmpt )

Standard deviation is a way of visualizing how spread out points of data are in a set. Using standard deviation helps to determine how rare or common an occurrence is. For example, data points falling within the boundaries of one standard deviation typically account for about 68% of data and those between (+/-)1 standard deviation and (+/-)2 standard deviations make about 27% combined. This can be better visualized by using a bell graph. Using the mean and standard deviation, the points where standard deviations occur can be drawn on the graph to better understand which data is rare and which is common.

Advisors and investors would do well to pay as much attention to the expected volatility of any portfolio or investment as they do to anticipated returns. Moreover, all things being equal, a new investment should only be added to a portfolio when it either reduces the expected risk for a targeted level of returns, or when it boosts expected portfolio returns without adding additional risk, as measured by the expected standard deviation of those returns. Lesson 2: Don’t assume bonds or international stocks offer adequate portfolio diversification. As the world’s financial markets become more closely correlated, bonds and foreign stocks may not provide adequate portfolio diversification. Instead, advisors may want to recommend that suitable investors add modest exposure to nontraditional investments such as hedge funds, private equity and real assets. Such exposure may bolster portfolio returns, while reducing overall risk, depending on how it is structured. Lesson 3: Be disciplined in adhering to asset allocation targets. The long-term benefits of portfolio diversification will only be realized if investors are disciplined in adhering to asset allocation guidelines. For this reason, it is recommended that advisors regularly revisit portfolio allocations and rebalance

“The Benefits of diversification are clear. Portfolio theory has played a crucial role in explaining the relationship between risk and return where more than one investment is held. It also enables us to identify optimal and efficient portfolios.”

Harry Markowitz 1991, developed a theory of “Portfolio choice”, that allows the investors to examine the risk as per the expected returns. In modern World, this theory is known as Modern portfolio theory (MPT). It attempts to attain the best portfolio expected return for a predefined portfolio risk, or to minimise the risk for the predefined expected returns, by a careful choice of assets. Though it’s a widely used theory, still has been challenged widely. The critics question the feasibility of theory as a strategy for

The prices of stocks are taken on daily basis and daily returns are calculated from it. The daily variances between these returns come out and the value at risk calculated from it with the percentile is applied on it. The value at risk tells you about the riskiness a price has on a portfolio. The positive outcome of this approach is the simplicity in implementation. The benefits of this method are its simplicity to implement and its negative aspect is that it requires a large amount of data for calculation which is extensive to calculate.

spread of scores from the mean (Burns & Grove, 2007). The larger the value of the standard deviation for study variables, the greater the dispersion or variability of the scores for the variable in a

Answer: The standard deviation tells about the difference between the actual value and the observed or the distance between two values.

The tighter the probability distribution of its expected future returns, the greater the risk of a given investment as measured by its standard deviation.

For standard deviation, we use it to measure the stand-alone risk of certain asset, which include both the systematic risk and unsystematic risk. However, when combining the assets into the portfolio, due to the correlation among the assets, certain amount of unsystematic risk could be diversified. Suppose all of the unsystematic risks could be diversified after the combination of the assets, we could use ß to measure each variable’s risk. So we have the ß of Vanguard for 0.98, the ß for Reynolds for 0.71 and the

When we measure risk per unit of return, Collections, with its low expected return, becomes the most risky stock. The CV is a better measure of an asset’s stand-alone risk than because CV considers both the expected value and the dispersion of a distribution—a security with a low expected return and a low standard deviation could have a higher chance of a loss than one with a high but a high .

To reduce a firm’s specific risk or residual risk a portfolio should have negative covariance or rather it should have no variance at all, for large portfolios however calculating variance requires greater and sophisticated computing power. As such, Index models greatly decrease the computations needed to calculate the optimum portfolio. The use of such Index models also eliminates illogical or rather absurd results. The Single Index model (SIM) and the Capital Asset Pricing Model (CAPM) are such models used to calculate the optimum portfolio.

According to the CAPM model:R_i=α+βR_m+ε, α represent the abnormal return gained by the portfolio. If the market is efficiency, the α has to be zero.

Even though there are flaws in the CAPM for empirical study, the approach of the linearity of expected return and risk is readily relevant. As Fama & French (2004:20) stated “… Markowitz’s portfolio model … is nevertheless a theoretical tour de force.” It could be seen that the study of this paper may possibly justify Fama & French’s study that stated the CAPM is insufficient in interpreting the expected return with respect to risk. This is due to the failure of considering the other market factors that would affect the stock price.

During 1952, Markowitz came out with a theory based on diversified investment is able to construct the risk-averse investors. He diversified investment portfolio theory and efficiency of the priory rigorous mathematical tools as a means to demonstrate risk-averse investors in a number of risky assets in construct the optimal portfolio methods.

If the assets exist to help meet a liability, the liability should be considered in the process; 3. Basing one’s decision solely on an asset allocation’s mean and variance is insufficient to base one’s decisions, in a world in which asset class returns are not normally distributed; and, 4. Most investors have multi-period objectives and the mean-variance framework is a single period model. These potential shortcomings are the likely reasons that practitioners have not fully embraced meanvariance optimization. For a number of practitioners, mean-variance optimization creates the illusion of quantitative sophistication; yet, in practice, asset allocations are developed using judgmental, ad hoc approaches. Recent advances significantly improve the quality of typical mean-variance optimizationbased asset allocations that should allow a far wider audience to realize the benefits of the Markowitz paradigm, or at least the intent of the paradigm. In this article, we focus on the first issue: the lack of diversification that can result from traditional meanvariance optimization. We begin with two examples in which traditional mean-variance optimization