Finance: Portfolio Variance, CAPM, and Investment Theories

The variance of a portfolio consisting of Securities 1 through 5, with weights W 1 through

W5, can be written as:

σP2 = W12σ12 + W22σ22 + W32σ32 + W42σ42

+ W52σ52

+ 2W1W2COV12 + 2W1W3COV13 + 2W1W4COV14 + 2W1W5COV15

+ 2W2W3COV23 + 2W2W4COV24 + 2W2W5COV25 + 2W3W4COV34

+ 2W3W5COV35 + 2W4W5COV45

True

The Efficient Frontier can be defined as consisting of those portfolios that offer the

highest return for a given level of risk, or the least risk for a given level of return.

True

A covariance matrix involving N securities will have [ (N)*(N) ] cells, [ N ] variance terms,

[ (N)(N-1) / 2 ] covariance terms, and [ (N)(N-1) / (N-1) ] pairs of covariance terms.

False

Assume that Securities A and B are expected to pay exactly the same dividend stream

over time. However, Security A has a beta of -1.50, while Security B has a beta of

+1.50. Because Security A has less risk than Security B (in fact, because of the negative

beta it has less risk than a risk-free security), its required rate of return will be less and

its price will be more than for Security B.

True

Fannie Mae uses duration to manage its interest rate risk. To do so, it attempts to

maximize the difference between the duration of its assets and the duration of its

liabilities. This help to maximize profits while immunizing or minimizing their exposure to

interest rate risk.

False

Prices of debt (fixed income) securities are directly related to the required rate of return.

As market interest rates (required rates of return) go up, the price of the security also

goes up.

False

If you constructed a variance/covariance matrix for the S&P 500, you would need to

calculate 500 variances and 124,750 pairs of covariances.

True

The variance of a 4-security portfolio can be calculated as follows:

σ2P = W12σ21 + W22σ22 + W32σ23 + W42σ24

+ W1W2σ1σ2COR12 + W1W3σ1σ3COR13 + W1W4σ1σ4COR14

+ W2W3σ2σ3COR23 + W2W4σ2σ4COR24 + W3W4σ3σ4COR34

False

Given a risk-free rate of 5 percent and an expected return on the market of 12 percent (a

market risk premium of 7 percent), a security with a beta of +2.0 will have a required rate

of return of 19 percent, while a security with a beta of -2.0 will have a required rate of

return of -9 percent.

True

The sinking of the PetroBras oil-drilling platform in March of 2001 is an example of

company, or idiosyncratic risk, since the risk was specifically related to PetroBras, and

not the market as a whole. And, as such, it could have been diversified away.

True

Because of flotation costs, the cost to the firm of debt financing, preferred stock, retained

earnings, newly issued equity, etc., will always be greater than the investors' comparable

required rates of return.

False

One common way of selecting a risk-adjusted discount rate for a project is simply to

make a subjective adjustment to the firms overall cost of capital: increase the rate for

higher-risk projects and decrease the rate for lower-risk projects.

True

Which of the following statements is not (or least) correct?

Although the beta of a diversified portfolio represents that risk which cannot be

diversified away, the beta of a single security, since it is not diversified, is a

measure of its total or stand-alone risk.

Select the statement that is most correct.

Assuming that everyone can lend and borrow at the same risk-free rate,

rational investors will hold a portfolio on the capital market line (i.e., a ray from

the risk-free rate that is tangent to the efficient frontier of risky securities).

Stock X has a beta of 0.5 and Stock Y has a beta of 1.5. Which of the following

statements is most correct?

If expected inflation increases (but the market risk premium is unchanged), the

required returns on the two stocks will increase by the same amount.

Which of the following statements is most correct?

A security's beta measures its non-diversifiable (systematic, or market) risk

relative to that of the market or an "average stock" within the market.

Which of the following statements is most correct?

Beta measures market risk, but if a firm's stockholders are not well diversified,

beta may not accurately measure stand-alone risk

The Gordon Growth Model, for evaluating the price of a share of common stock, may

also be used to find the price of preferred stock or any other perpetuity.

True

Because of diversification, a completely diversified portfolio of stocks has no market risk.

False

In the CAPM, the risk-free rate is multiplied by the stock's beta coefficient to determine

the additional risk premium that is required by investors for the risk inherent in the stock.

False

Dell Corporation would be involved in a spot market transaction if it were to agree today

to sell 500 computers, seven months from now at a price of $500 each, to Best Buy.

False

The degree of investors' risk aversion will have no effect on the security market line.

False

All other factors held constant, the higher a security's market risk, the higher its required

rate of return, and the lower its price.

True

The Gordon Dividend Growth Model can be defined as [ D1 / KS - g ]. However, for this

model to work, the growth rate (g) must be positive and less than the required rate of

return (KS).

False

We can define the long-run sustainable growth rate of a firm as a function of the firm's

retention rate and the firm's return on equity.

True

The retention rate of the firm is equivalent to the dividend payout rate of the firm.

False

In general, we can say that undiversified stockholders, including the owners of small

businesses, are more concerned about corporate risk than market risk.

True

To use the Gordon, constant growth model to evaluate the price of a firm's stock, based

on the present value of the dividends to be paid on the stock, we must assume that the

long-run sustainable growth rate of dividends is less than the investors' required rate of

return. If we do not, we may easily get nonsensical results.

True

No rational investor should be willing to pay for a share of stock where the dividend is

expected to decrease constantly over time.

False

If Stocks J and K are constant growth stocks, and have the same required rate of return,

but the price of Stock J is lower than the price of Stock K, then Stock J must have a

higher expected dividend yield.

False

If Stocks J and K are constant growth stocks, and have the same required rate of return,

but the price of Stock J is lower than the price of Stock K, then Stock J must have a

lower expected dividend yield.

False

If a stock is in constant growth, then the growth rate of its price (price appreciation or

capital gain) is exactly the same as the growth rate of its dividends.

True

If a stock is in constant growth, then the growth rate of its dividends will be exactly the

same as its expected dividend yield.

False

Which of the following statements is not (or least) correct?

In order to use the constant growth model to evaluate the price of a share of

common stock, we must assume that the investor's required rate of return will

be less than the long-run constant growth rate.

Select the statement that is most correct.

Markets are in equilibrium when supply is equal to demand. This is also where

investors' required rates of return are equal to expected rates of return.

Select the statement that is most correct.

To find the current price of a supernormal growth stock, we must value both the

dividends during the supernormal period as well as the price at the end of the

supernormal period (equivalent to the value of the remaining dividend stream

out to infinity), where both have been discounted to the present

If two constant growth stocks have the same required rate of return and the same price,

which of the following statements is most correct?

The stock with the higher dividend yield will have a lower dividend growth rate.

Select the statement that is most correct.

The constant growth model used for evaluating the price of a share of common

stock may also be used to find the price of perpetual preferred stock or any

other perpetuity.

Stocks A and B have the same required rate of return and the same expected year-end

dividend (D1). Stock A's dividend is expected to grow at a constant rate of 10 percent

per year, while Stock B's dividend is expected to grow at a constant rate of 5 percent

per year. Which of the following statements is most correct?

A. The two stocks should sell at the same price.

B. Stock A has a higher dividend yield than Stock B.

C. Currently Stock B has a higher price, but over time Stock A will eventually have

a higher price.

D. Statements B and C are correct.

* E. None of the statements above is correct.

Select the statement that is most correct.

The SML relates required returns to the firms' market risk. The slope and

intercept of this line cannot be controlled by the financial manager.

Which of the following statements is incorrect (least correct)?

The price sensitivity of a share of common stock increases with the time

remaining until it matures.

When calculating a WACC for a company with preferred stock, there is no need to

adjust the cost of the preferred stock to reflect the tax exclusion of 70% of the

preferred stock dividend.

True

A firm can only have one break point in its marginal cost of capital curve, which will

occur when they deplete their additions to retained earnings and must switch over to

new issues of equity.

False

Because creditors can foresee, to at least some extent, the costs of bankruptcy, they

charge a higher rate of interest to compensate for the present value of bankruptcy costs.

True

Increasing a company's debt ratio will typically reduce the marginal cost of both debt and

equity financing; however, it still may raise the company's WACC.

False

Although quite rare, the mathematics is such that the after-tax component cost of debt

financing can be greater than the after-tax component cost of equity financing.

False

The cost to the firm of retained earnings is zero, since they are generated from the

current earnings of the firm and there are no flotation costs associated with their

retention.

False

If we assume that the stock market is efficient, and if we assume that Stock A has a beta

of 1.20, while Stock B has a beta of 1.40 (that is, B has higher risk than A), then we mustalso assume that the required rate of return on Stock B exceeds the required rate of

return on Stock A.

True

If a firm must pay flotation expense when issuing a security, then the firm's required rate

of return on that security will be greater than the investor's required rate of return for that

security.

True

The easiest way to correctly calculate the firm's cost of debt is simply to multiply the

coupon rate on the debt times one minus the firm's tax rate.

False

The cost of equity capital from the sale of new common stock (r e) is generally equal to

the cost of equity capital from retention of earnings (r s), divided by one minus the

flotation cost as a percentage of sales price (1 - F).

False

If expectations for long-term inflation rose, but the slope of the SML remained constant,

this, for most firms, would have a greater impact on the required rate of return on equity,

rs, than on the interest rate on long-term debt, rd. In other words, the percentage point

increase in the cost of equity would be greater than the increase in the interest rate on

long-term debt. (Hint: play with some numbers and see what happens.)

False

If the tax laws stated that $0.50 out of every $1.00 of interest paid by a corporation

was allowed as a tax-deductible expense, it would probably encourage companies to

use more debt financing than they presently do, other things held constant.

False

Which of the following statements is not (or least) correct?

Because of the tax shelter created by issuing preferred stock dividends

(remember that 70 percent of dividends are excluded from taxes), the firm's

after-tax cost of preferred stock may be significantly less than its before-tax

cost

If a U.S. company with two divisions, one very risky and the other with significantly less

risky, uses the same corporate discount rate to evaluate all projects, the most likely

outcome, as discussed in class, is that the firm will become:

Riskier over time, and its value will decline.

A firm is considering the purchase of an asset whose risk is greater than the current

risk of the firm, based on any method for assessing risk. In evaluating this asset, the

decision maker should:

Increase the cost of capital used to evaluate the project to reflect the higher risk

of the project.

Select the statement that is most correct

When calculating the cost of debt, a company needs to adjust for taxes,

because interest payments are tax deductible.

Select the statement that is most correct.

All other things equal (including component costs), a higher tax rate will lower a

firm's WACC only if the firm uses debt financing.

Which of the following statements is most correct?

The "enterprise" value of the firm can be found by taking the free cash flow

available to all investor's and discounting it at the firm's weighted average cost

of capital.

Which of the following statements is most correct?

If a company's tax rate increases but the yield to maturity of its noncallable

bonds remains the same, then, all other factors held constant, the firm's WACC

should decrease

Which of the following statements is correct (most correct)?

A company's targeted capital structure will affect its cost of capital. Changes

from the target may cause the weighted average cost of capital to either

increase or decrease.

Select the statement that is most correct.

The component costs of capital are market-determined variables in as much as

they are based on investors' required returns.

A firm with financial leverage will have a larger equity multiplier than an otherwise

identical firm with no debt in its capital structure.

True

If a company were to issue debt and use the proceeds to increase assets, and if the

company's return on assets (ROA) remained the same, then the return on equity (ROE)

would increase.

True

If certain ratios for a firm's assets, such as accounts receivable turnover, inventory

turnover, total asset turnover, etc., are generally constant over time, then the level

(amount) of these assets can also be expressed as a percentage of sales.

True

Since ROA measures the firm's effective utilization of assets (without considering how

these assets are financed), two firms with the same net income must have the same

ROA.

False

Retained earnings is the cash that has been generated by the firm through its

operations which has not been paid out to stockholders as dividends. Retained

earnings are kept in cash or near cash accounts and thus, these cash accounts, when

added together, will always be equal to the total retained earnings of the firm.

False

In accounting, emphasis is placed on determining net income. In finance, the primary

emphasis is also on net income because that is what investors use to value the firm.

However, a secondary consideration is cash flow because that's what is used to run

the business

False

Since ROA measures the firm's effective utilization of assets (without considering how

these assets are financed), two firms with the same EBIT must have the same ROA.

False

Suppose a firm wants to maintain a specific TIE ratio. If the firm knows the level of its

debt, the interest rate it will pay on that debt, and the applicable tax rate, the firm can

then calculate the earnings level required to maintain its target TIE ratio.

True

One of the problems of ratio analysis is that account relationships can be manipulated.

For example, we know that if we use some of our cash to pay off some of our current

liabilities, the current ratio will always increase, especially if the current ratio is low

initially, for example, below 1.0.

False

Your company recently issued new common stock and used the proceeds to reduce its

short-term notes payable and accounts payable. This action had no effect on the

company's total assets or operating income. Determine which of the following effects

did occur as a result of this action.

E. The company's equity multiplier decreased.

You have collected the following information regarding Companies C and D:

• The two companies have the same total assets.

• The two companies have the same operating income (EBIT).

• The two companies have the same tax rate.

• Company C has a higher debt ratio and interest expense than Company D.

• Company C has a lower profit margin than Company D.

On the basis of this information, select the statement that is most correct

Company C must have a lower ROA.

Company A's current ratio is 0.5, while Company B's current ratio is 1.5. Both firms

want to "window dress" their coming end-of-year financial statements. As part of its

window dressing strategy, each firm will double its current liabilities by adding short-

term debt and placing the funds obtained in the cash account. Which of the

statements below best describes the actual results of these transactions? (Hint: you

may wish to construct some simple numerical examples.)

Only Company A's current ratio will be increased.

Company A and Company B have the same tax rate, total assets, and basic earning

power. Both companies have positive net incomes. Company A has a higher debt

ratio, and therefore, higher interest expense than Company B. Which of the following

statements is most correct?

Company A pays less in taxes than Company B.

Your company recently issued new common stock and used the proceeds to reduce its

short-term notes payable and accounts payable. This action had no effect on the

company's total assets or operating income. Which of the following effects did occur

as a result of this action?

The company's equity multiplier decreased

Which of the following statements is least correct (most incorrect)?

In an inflationary environment, a firm's use of FIFO rather than LIFO can lead

to higher reported earnings, higher taxes, and lower cash flows. In the same

manner, basing depreciation expense on historical costs rather than actual

replacement values in an inflationary environment may lead to lower reported

earnings, lower taxes, and higher cash flows.

Which of the following statements is most incorrect

Assume that a firm has had a decreasing P/E ratio for the last three years.

When its P/E finally drops below the P/E for its industry, it will clearly be

undervalued and a good buy for your investment portfolio.

Which of the following statements is most correct?

In an inflationary environment, a firm is better off if it is a net debtor (owes more

money than is owed to it) rather than a net creditor (owes less money than is

owed to it).

Which of the following statements is most incorrect

An increase in debt and interest expense will lead to a higher ROA for a firm,

all other factors held constant, but this increase in leverage may lower the

firm's ROE.

Assume that a firm is profitable (positive net income) and that it increases its use of

short-term debt (notes payable) and invests the proceeds in assets that earn a return

greater than the firm's weighted average cost of capital. Which of the following would

you most expect to observe?

An increase in economic value added (EVA)

Dissagregation of ROA and ROE allows us to do all of the following except:

Determine whether the firm has effectively traded off its current ratio against its

debt ratio to maximize its ROE

Which of the following statements concerning LIFO versus FIFO is most correct if a

firm has been operating in an inflationary environment?

Firms that use FIFO will appear to have a stronger balance sheet (at least in

terms of inventory) than if they used LIFO: this may be best when trying to

arrange loans from creditors, such as banks, that look at the value of inventory

as collateral.

Company A and Company B have the same total assets, the same total assets

turnover, and the same return on equity. However, Company A has a higher return on

assets than Company B. Given this information, determine which of the following

statements is most correct

Company A has a higher profit margin and a lower debt ratio than Company B.

Still learning (1)

You've started learning these terms. Keep it up!