## Portfolios Of Two Risky Assets

In the last section we considered naive diversification using equally weighted portfolios of several securities. It is time now to study efficient diversification, whereby we construct risky portfolios to provide the lowest possible risk for any given level of expected return. Portfolios of two risky assets are relatively easy to analyze, and they illustrate the principles and considerations that apply to portfolios of many assets. We will consider a portfolio comprised of two mutual funds, a...

## The Optimal Risky Portfolio with Two Risky Assets and a Risk Free Asset

What if our risky assets are still confined to the bond and stock funds, but now we can also invest in risk-free T-bills yielding 5 We start with a graphical solution. Figure 8.6 shows the opportunity set based on the properties of the bond and stock funds, using the data from Table 8.1. Two possible capital allocation lines CALs are drawn from the risk-free rate rf 5 to two feasible portfolios. The first possible CAL is drawn through the minimum-variance portfolio A, which is invested 82 in...

## Forecasting the Stock Market

What can we learn from all of this about the future rate of return on stocks First, a note of optimism. Although timing the stock market is a very difficult and risky game, it may not be impossible. For example, we saw in Chapter 12 that some variables such as the market dividend yield seem to predict market returns. However, if market history teaches us anything at all, it is that the market has great variability. Thus, although we can use a variety of methods to derive a best forecast of the...

## Optimal Portfolios With Restrictions On The Riskfree Asset

The availability of a risk-free asset greatly simplifies the portfolio decision. When all investors can borrow and lend at that risk-free rate, we are led to a unique optimal risky portfolio that is appropriate for all investors given a common input list. This portfolio maximizes the reward-to-variability ratio. All investors use the same risky portfolio and differ only in the proportion they invest in it versus in the risk-free asset. What if a risk-free asset is not available Although T-bills...

## Survivorship Bias And Tests Of Market Efficiency

We've seen that survivorship bias might be one source of the equity premium puzzle. It turns out that survivorship bias also can affect our measurement of persistence in stock market returns, an issue that is crucial for tests of market efficiency. For a demonstration of the potential impact of survivorship bias, imagine that a new group of mutual funds is set up. Half the funds are managed aggressively and the other conservatively however, none of the managers are able to beat the market in...

## Spot And Forward Yields

The spreadsheet entitled SPOTYA.XLS, found on the Online Learning Center www.mhhe.com bkm , can be used to estimate spot rates from coupon bonds and to calculate the forward rates for both single-year and multiyear bonds. The spreadsheet demonstrates a methodology to bootstrap spot rates from coupon bonds. The model sequentially solves for the spot rates that are associated with each of the periods. The methodology is similar to but slightly different from the regression methodology described...

## Find The Equilibrium Expected Excess Return On This Stock Using The

We have assumed so far that there is only one systematic factor affecting stock returns. This simplifying assumption is in fact too simplistic. It is easy to think of several factors driven by the business cycle that might affect stock returns interest rate fluctuations, inflation rates, oil prices, and so on. Presumably, exposure to any of these factors will affect a stock's risk and hence its expected return. We can derive a multifactor version of the APT to accommodate these multiple sources...

## Financial Leverage and ROE

An analyst interpreting the past behavior of a firm's ROE or forecasting its future value must pay careful attention to the firm's debt-equity mix and to the interest rate on its debt. An example will show why. Suppose Nodett is a firm that is all-equity financed and has total assets of 100 million. Assume it pays corporate taxes at the rate of 40 of taxable earnings. Table 19.4 shows the behavior of sales, earnings before interest and taxes, and net profits under three scenarios representing...