Summary of Chapters
Chapter 7: Mathematics of Investing
One of the return measures used includes compounding. Compounding can be done arithmetically or geometrically. In order for one to determine whether to use arithmetic compounding or geometric compounding one has to take into account the future value of what is to be estimated (Evensky, Horan, and Robinson 122). Arithmetic compounding is best used when determining the estimate of the anticipated future return for the following year when there is no other information. The geometric compounding is best applied when determining the anticipated return over many periods.
This is applied when investments in a combined portfolio do not move in the same direction. One investment performs well while another performs poorly. The measure of this difference in a combined portfolio is referred to as covariance. The covariance is calculated by using the sum of the product of deviations for each investment and then dividing by the number of observations.
This technique is applied to determine the relationship between investments. A regression equation is usually developed to provide details of correlation. For instance, in a market situation, the value of beta greater than 1 indicates that there is a higher risk in the market while that lower than 1 indicates that the level of risk is low.
Higher moments can be described by the use of skewness and kurtosis. Skewness measures the asymmetry of the distribution of returns. Kurtosis provides information of the peak and low returns.
Performance Measures ratios
In assessing the level of risk and returns in investments, several ratios can be used (Evensky, Horan, and Robinson 141). These include the Sharpe ratio, information ratio, Treynor ratio, Sortino ratio, and the Alpha-Jensen’s Differential Return Measure.
Chapter 8: Investment Theory
Modern Portfolio Theory
This is an investment theory that is based on a theoretical mathematical model. In this theory, a number of assumptions are used. One of the assumptions is that investors are rational, thus will want to maximize the expected utility of their investments. Secondly, to maximize their expected utility on investments, the investors will select investments based on their evaluation of risks and returns. Thirdly, rational investors will choose the lowest risk for a given return and will select the highest return for a given risk. Fourthly, return in this case is measured as total return. Fifthly, risk is defined as the uncertainty of return as is measured by variance. Additionally, investors choose their assets from a multitude of risky assets.
Limitations of the Modern Portfolio Theory
One of the limitations of this theory is that investors can choose to select investments that are not risky at all. Further, the investors may not only be rational but can also be irrational. Another limitation is that market returns are not usually normally distributed. Additionally, there is no accepted multitude of risky assets. The investors will also be more concerned with the downside risk more than the total risk. Further, the risks and returns of a particular security cannot be known in advance.
Capital Market Theory
Based on the Capital market theory an investor needs to invest in a combination of two investments. These are the market portfolio and the risk free asset. Risk in this case has two components, the systematic risk, and the unsystematic risk. Systematic risk is related to the market and cannot be diversified. Unsystematic risk is a risk that can be removed through diversification.
The chaos theory has a significant impact in the capital markets. One of these implications is that the chaotic system, despite being highly structured can change unexpectedly. This creates a false faith in successfully back-tested trading systems. Secondly, accurate forecasting of returns is not achievable. Thirdly, chaotic markets follow certain mathematical rules, which utilize an information feedback mechanism.
Chapter 10 Portfolio Optimization
Mean Variance Optimization
In the optimization of returns, managers are required to make a decision regarding the investment time horizon and estimates of the asset class included in the portfolio. Important issues to consider in the portfolio include expected return, expected standard deviation, and expected correlation among the asset classes. It is expected that the estimates of the expected return and standard deviation should match the time horizon that is stipulated in the investment policy of the investor. Thus, time horizon of the investor normally is longer, and optimization is based on these long time horizons. Therefore using a mean variance optimization will enable the use of standard deviation as a measure of volatility.
Return inputs are estimated using historical experience, and risk premium approach. Historical experience works on the assumption that future returns will be the same as past returns. The risk premium approach is based on the level of risk in the investment. The extra return that investors acquire for investing is referred to as risk premiums.
This is applied when certain conditions regarding the investment have changed. The most common rebalancing is client induced. The portfolio is rebalanced based on the changes or circumstances that have affected the client. These changes may include inheritance of a large amount of money and these necessitate the need to evaluate the client’s goals of investment and strategies.
Focusing too much on the mean variance as a risk measure may have its limitations. Increased research in investment theory has provided information that provides evidence that the standard deviation is not essentially an acceptable measure of risk. This challenges the scenario in the modern portfolio theory where optimization is dependent on the standard deviation. Further, most of the return distributions are not normally distributed, which makes use of mean variance limited since it is based on normal distributions only.
Chapter 12 Retirement Planning
Retirement planning is aimed towards providing a form of income to the client during retirement. The need for retirement planning has increased since income programs provided by governments are declining and their future is uncertain. One of the approaches used in retirement planning is the capital needs analysis. This method is used to evaluate the client’s retirement goals. The analysis provides information regarding the ability of the client’s current portfolio to satisfy his or her future financial requirements. The analysis covers preretirement savings, preretirement expenses, preretirement income, preretirement liquidity needs, and expenses after retirement, income after retirement and the required retirement distributions (Evensky, Horan, and Robinson 271). Further, there is also need of taking into account inflation and taxation rates in the analysis. Liability of retirement is estimated using the Monte Carlo approach.
Individual Retirement Accounts
Individual retirement’s accounts include the traditional IRA and the Roth IRA. The type of the IRA affects the income growth, tax rates, and pension income. According to Evensky, Horan, and Robinson (284), Roth IRA provides high-income replacements. This is best suited for the aggressive savers. For the less aggressive savers, the traditional IRA is best since they enjoy modest withdrawal tax rate.
The risks that need to be managed during retirement include medical expenses, inflation risk, and longevity risk. Longevity risk is quite uncertain and old people are likely to die than young people. Inflation may cause the real value of fixed annuities to decrease. Medical risk expense requires the application of health insurance to manage the risk of unpredictable medical costs.
Evensky, Harold, and Stephen M. Horan. The new wealth management: the financial advisor's
Guide to managing and investing client assets. Hoboken, N.J.: J. Wiley & Sons, 2011. Print.