Certainly, many books have them, but this book would have only two or three that get to the heart of the issues discussed in this chapter. Their need to understand financial concepts and tools at the user level was constantly on my mind as I wrote this book.
RISK AND RETURN
BASIC CONCEPTS
Also note that the more frequent the compounding, the more money we get at the end of the year. 3 Return to Table 1.3 and fill in the blanks in the fifth column by calculating GE's annual continuously compounded returns.
MEAN RETURNS
In general, the arithmetic mean return (AM) of any series of returns is given by Not surprisingly, the internal rate of return on our investment is equal to the stock's geometric mean rate of return.
TOTAL RISK
One way to formally capture this volatility is to calculate the standard deviation of returns (SD), which (hold on to your seat) is the square root of the mean squared deviation of the arithmetic mean return. Let's take a quick look at calculating the standard deviation of returns from Intel.
RISK AND RETURN I
PORTFOLIOS
Would you choose a portfolio on the lower branch of the feasible set (ie, the branch descending from the MVP). Regardless of the number of assets, a portfolio's return is always equal to the weighted average of the returns of all assets in the portfolio.
DIVERSIFICATION
Take a look at Figure 5.1, which shows the returns of stocks 1 and 2, as well as the return of the proposed portfolio (the dotted line). In all other cases, the risk of the portfolio is lower than the weighted average of the risks.
SYSTEMATIC RISK
In a two-stock portfolio, events that affect the price of both stocks only partially affect the risk of the portfolio. It follows, as a mathematical necessity, that each stock contributes less to the risk of the portfolio than the total risk. That is how we measure the risk of a stock that is part of a portfolio: by its (absolute or relative) contribution to the risk of the portfolio.
In other words, as the number of assets grows, the risk of the portfolio is largely determined by covariances and largely independent of variances. Suppose we have a fully diversified portfolio of US stocks and we are therefore subject to the systematic risk of the US economy. Make a graph with the number of stocks on the x-axis and the standard deviation of the portfolio on the y-axis.
RISK AND RETURN II: THE CAPM AND THE COST OF CAPITAL
The risk-free interest rate is the compensation for the expected loss of purchasing power, while the risk premium is the compensation for taking on the asset's risk. This means that we need forward-looking estimates of the risk-free rate, market risk premium and beta. Although this does not pose a risk-free rate problem, forward-looking estimates of the market risk premium and beta are not easily obtained.
To estimate the required return on any stock, equation (7.4) requires an estimate of the risk-free rate, secondly an estimate of the market risk premium (both common to all firms), and secondly an estimate of the stock's beta (specific to each firm). ). Finally, the debt that is considered when estimating the cost of capital is interest-bearing (usually long-term) debt. 2 Using a risk-free rate of 4.3% (the 10-year Treasury note yield at the end of 2003) and a market risk premium of 5.5%, calculate the required return on capital of the three companies in question 1 using the CAPM. .
RISK AND RETURN III
ALTERNATIVES TO THE CAPM
Also remember that this is measured by the average historical difference between the return of the market portfolio (a widely accepted benchmark index of stocks) and the risk-free rate. And finally, remember that 'the sensitivity of stock returns is measured to changes in the market risk premium (or, simply, to changes in the market's return). Let's start with what we already know from the previous chapter on estimating the CAPM.
And let's do it, as in the previous chapter, for the 30 stocks of the Dow. The sixth column of Table 8.2 shows the required return on equity of the 30 Dow companies estimated with the three-factor model using equation (7.5). The three-factor model is the main contender of the CAPM and its popularity has steadily increased.
DOWNSIDE RISK
And the square root of the variance is the standard deviation of the returns; in this case 90.9%. The last column of Table 9.1 shows the square of the numbers in the fifth column. If the variable X follows a normal distribution, the calculation of VaR is very simple indeed.
Following the same steps, you can calculate the rest of the VaRs shown in Table 9.4. If it is not, then the calculation of VaR is more complicated than indicated by equation (9.3). 1 Consider the annual returns of the Chinese and Korean markets (both aggregated from the MSCI indices, in dollars and accounting for both capital gains and dividends) during 1994 and 2003 shown in Table 9.4. a) Calculate the (arithmetic) mean and standard deviation of both markets.
RISK AND RETURN IV
RISK-ADJUSTED RETURNS
Suppose we rank funds based on their risk-adjusted long-term performance. The Jensen Index is a widely used measure of risk-adjusted fund performance, but it is not without its problems. The Sharpe ratio is undoubtedly one of the most widely used tools for assessing the risk-adjusted performance of funds.
Note that the RAPs in Table 10.2 indicate that all funds outperformed the market on a risk-adjusted basis. Our final measure of risk-adjusted returns is very similar to the Treynor ratio and the Sharpe ratio, but uses a different definition of risk. This table also shows that the ranking of funds based on their Sortino ratio differs from the rankings based on our previous measures of risk-adjusted returns.
RISK AND RETURN V
OPTIMAL PORTFOLIOS
The first line states the objective, which (as in the previous problem) is to find the portfolio with the least risk. The first line states the objective, which is to find the portfolio with the highest expected return. The second row specifies the constraint that the portfolio must have a target risk level of SDT.
Note that increasing a portfolio's expected return or decreasing its risk will increase the Sharpe ratio. The first line states the objective, which is to find the portfolio with the highest Sharpe ratio, and the second line states the allocation constraint. In all questions it is implicitly stated that the constraint x1+x2+x3+x4= 1 must hold.). a) Find the portfolio with the highest risk-adjusted return.
RISK AND RETURN VI
THE LONG RUN
If we consider each five-year holding period instead, we'd get 28.6% at best. By the way, note in Exhibit 12.1 that the average annual compounded return of the worst 20-year and 30-year US holding periods was 3% and 5%, respectively, both positive and higher than inflation.). The idea behind annual standard deviation as a measure of long-term risk is that as the investment period increases, the dispersion around the long-term mean compounded return decreases.
The distribution of annual, continuously compounded returns has an arithmetic mean of 8.6% and a standard deviation of 16.8%. Therefore, in equation (12.3) we have annual quantities in the numerator, and the annualized standard deviation in the denominator. In the US, it is clear that as holding periods increase, the number of periods in which equities underperformed bonds decreases.
VALUATION
THE DIVIDEND DISCOUNT MODEL
The numerator of the last term is the terminal value and therefore an estimate of the stock price at time T. In the long run, the growth of dividends, the growth of profits and the growth of the value of the company should be in line. That becomes an upper bound for any plausible estimate of long-term dividend growth.
Note that, in this case, the current value of the terminal value is approximately 60% of our estimated intrinsic value of. Note that for the DDM to provide an accurate estimate of intrinsic value, everything relevant to the company's valuation must be summed up in a sequence of dividends. For an estimate of the market risk premium you can use 5.5%, as we did in the text for the analysis of GE.). a) Estimate the appropriate discount rate for DDM.
THE WACC MODEL
We can think of EFCF as cash for a company's shareholders. The debt considered for estimating the cost of capital is interest-bearing (usually long-term) debt. Third, it is essential to note that equation (14.3) does not give the value of the company's equity, but the value of the debt equity.
Therefore, to get an estimate of Dell's equity value, we must subtract from this figure the market value of its long-term debt. The WACC model is the most widely used version of the DCF model, and for good reason. So it delivers the value of the entire company, and not just the value of its equity.
OTHER DCF MODELS
This means that to determine the value of the company's equity, we must subtract the market value of the long-term debt from the calculated present value. Second, the discount rate is easier to estimate simply because it is only one component of the company's cost of capital. You may also recall that unlike the EFCF, the CFCF is independent of the company's capital structure.
Note that the FTE model, in the way it is usually implemented, provides the value of the company's equity. Let's apply the FTE model to the valuation of Dell at the beginning of the year 2004, using all the information we discussed in the previous chapter. As you may have noticed, these are the same assumptions we made for the expected growth of the CFCFs in the previous chapter.).