Unit 4 & 5

One dollar invested in a portfolio of long-term U.S government bonds in 1900 would have grown in nominal value by the end of year 2011 to:

$245

How can individual investors diversify?

A very simple way for an individual investor to diversify is to buy shares in a mutual fund that holds a diversified portfolio.

Discuss the importance of beta as a measure of risk

Beta is a measure of market risk. It is also called the relative measure of risk as it measures risk relative to the market portfolio. Beta is useful as a measure of risk in the context of well-diversified portfolios. It measures the risk contribution of a single security to the portfolio.

Explain why international stocks may have high standard deviations but low betas.

Beta is traditionally measured relative to the S&P 500 index. As such, there may be a weaker statistical relatinship between the S&P 500 and an international stock. If these two assets are mostly independent of one another, there is little chance they will have a statistically significant covariance. With a low covariance, by definition, the stock will have a low beta. This could occur even if the standard deviation of the beta is very high. This answer assumes that the market risk of domestic stocks is largely independent of the market risk in international stocks.

Briefly explain how diversification reduces risk.

Diversification reduces risk because prices of different securities do not move exactly together. When you form portfolios using a large number of stocks, the variability of the portfolio is much less than the average variability of individual stocks.

Briefly explainwhat the beta of a stock means

For each additional 1% change in the market return, the return on the stock on average changes by beta times 1%. For example, if the beta of IBM is 1.59, then for an additional 1% change in the market return, the expected change in the return of IBM stock will equal 1.59%.

What has the average annual nominal rate of interest on Treasury bills over the past 111 years (1900-2011)?

Greater than 3%

Average annual rate of return in real terms for a portfolio of U.S common stocks between 1900 and 2011?

Greater than 8%

Briefly explain the concept of value additivity.

If the capital market establishes a value PV(A) for asset A and PV(B) for asset B, the market value of a firm that holds both these assets is given by : PV(AB) = PV(A) + PV(B).. This logic can be extended for any number of assets. Value additivity is also applicable to cash flows. We can add the present values of two separate cash flows and et the present value of the combined cash flows. It can be stated as follows: PV(A+B) = PV(A) + PV(B) and PV(A+B+C) = PV(A) + PV(B) + PV(C). This idea can be extended for any number of cash flows.

In the formula for calculating the variance of an N-stock portfolio, how many covariance and variance terms are there?

In the formula for calculating the variance of an N-stock portfolio, there are [N(n-1)]/2 different covariance terms and N variance terms.

Briefly explain how the beta of a stock is estimated.

One can estimate the beta of a stock by plotting the market returns on the x-axis and the corresponding stock returns on the y-axis. The slope of the resulting line of best fit is the beta estimate for the stock. [Beta = Cov(Ri,Rm)/Var(Rm)\

What is the beta of a portfolio with a large number of randomly selected stocks>

The beta of a portfolio with a large number of randomly selected stocks equals one. The standard deviation of such a portfolio is equal to the standard deviation of the market.

Define the term "Risk Premium"

The difference between the security return and the risk-free rate such as a Treasury bill return, is called the risk premium. This denotes the additional return on the security because of additional risk.

Briefly explain how individual securities affect portfolio risk.

The risk of a well-diversified portfolio depends on the market risk of the securities included in the portfolio. Portfolio beta is the weighted average of individual security betas included in the portfollio. Individual securities affect portfolio risk to the extent that they change the beta of the portfolio.

Estimate of standard error

The standard deviation of returns divided by the square root of the number of observations.

Regarding stock returns, briefly explain the term "Variance"

Variance is a standard statistical measure of spread. The variance is the expected squared deviation from the expected return. From a finance point of view, this measures the total risk of a portfolio: the higher the variance, the higher risk of the portfolio. This is also called a measure of total risk.

Briefly explain the difference between beta as a measure of risk and variance as a measure of risk.

Variance measures the total risk of a security and is a measure of stand-alone risk. Total risk has both unique risk and market risk. In a well-diversified portfolio, unique risks tend to cancel each other out and only market risk remains. Beta is a measure of market risk and is useful in the context of a well-diversified portfolio. Beta measures the sensitivity of the security returns to changes in market returns. The market portfolio has a beta of one and thus has average risk.

For long-term U.S government bonds, which risk concerns investors the most?

a. Interest Rate Risk