# Investment Fundamentals and Portfolio Management questions

1. John Smith has been reviewing the stock of ABC. John has estimated that the stock will have the following possible returns and probabilities:

Return Probability

-0.15 0.10

-0.05 0.20

0.05 0.35

0.15 0.25

0.25 0.10

a. Compute the expected return on ABC stock.

b. Compute the standard deviation of returns on ABC.

2. A stock sells for $67 per share and pays a quarterly dividend of $0.50. One year later, the stock sells for $76.

a. Compute the holding-period return on this investment.

b. Compute the holding period return assuming that the investor could buy this stock borrowing half of the purchase price at 12 percent per annum interest.

c. Compute the holding period return (including the information from part b) if the investor pays a commission of $0.40 per share on both the purchase and sale transaction.

3. You open a margin account with a brokerage firm. The initial margin requirement is 50 percent, and the maintenance margin requirement is 25 percent. You purchase 100 shares of a stock selling for $40 per share.

a. How much money do you need to have in your margin account to make this purchase? (Ignore commissions.)

b. What is the amount of your margin loan from the broker?

c. If the stock falls to $32, what is the margin in the account?

d. At what stock price will you receive a margin call?

4. What is the market price per share of Whopie, Inc. if the firm had net income of $200,000, earnings per share of $2.70, total equity of $800,000, and a market to book value ratio of 1.5?

5. The companies in the electrical parts industry have an average earnings multiple of 16. John's Parts, Inc. manufactures electrical parts, and you have forecast that the company will earn $3.60 per share and its stock will sell at the industry average multiple 3 years from now. Estimate the value of John's Parts stock in 3 years. If the required rate of return is 14 percent, what is the present value of John's Parts stock?

6. Tom Jones has identified the following securities for a portfolio:

Security Amount Invested Expected Return Beta

A $25,000 0.05 1.4

B $35,000 0.11 0.1

C $5,000 0.15 0.5

D $35,000 0.01 1.9

Compute the expected return of the portfolio. Compute the beta of the portfolio.

7. The Elvis Alive Corporation, makers of Elvis memorabilia, has a beta of 2.35. The return on the market portfolio is 13%, and the risk-free rate is 7%. According to CAPM, what is the risk premium on a stock with a beta of 1.0?

8. Discuss the 3 forms of market efficiency and the evidence for each form of market efficiency.

9. Compute the value of the following options at expiration:

a. An IBM July 90 call when IBM sells for $98

b. An Eastman Kodak April 25 call with the stock priced at $19

c. A Wall-Mart January 60 put with Wal-Mart stock selling for $48

d. A Pfizer October 35 put with the stock priced at $42.

https://brainmass.com/economics/risk-management/176770

#### Solution Preview

Please see attached file for complete answers

1. John Smith has been reviewing the stock of ABC. John has estimated that the stock will have the following possible returns and probabilities:

Return Probability

-0.15 0.1

-0.05 0.2

0.05 0.35

0.15 0.25

0.25 0.1

a. Compute the expected return on ABC stock. 0.055

b. Compute the standard deviation of returns on ABC. 0.1117

(See calculations below)

ABC

return Probability return x Probability Difference from mean, i.e.0.055 Difference 2 Prob x Difference 2

-0.15 0.1 -0.0150 -0.2050 0.042025 0.0042025

=-0.15x0.1 =-0.15-0.055 =-0.205^2 =0.1x0.042025

-0.05 0.2 -0.0100 -0.1050 0.011025 0.0022050

0.05 0.35 0.0175 -0.0050 0.000025 0.0000087

0.15 0.25 0.0375 0.0950 0.009025 0.0022563

0.25 0.1 0.0250 0.1950 0.038025 0.0038025

Total 1.00 0.0550 0.012475

Expected return= 0.0550

Variance= 0.012475

Standard deviation of returns =square root of Variance= 0.1117 =square root of 0.012475

2. A stock sells for $67 per share and pays a quarterly dividend of $0.50. One year later, the stock sells for $76.

a. Compute the holding-period return on this investment.

Dividend income = 4 x $0.50= $2.00

Capital gains= $76- $67= $9.00

$11.00

Initial investment= $67.00

Therefore holding period return= 16.42% =11/67

b. Compute the holding period return assuming that the investor could buy this stock borrowing half of the purchase price at 12 percent per annum interest.

Amount borrowed=$67/2= $33.50

Interest @ 12% = $4.02 =0.12x33.5

Dividend income = 4 x $0.50= $2.00

Capital gains= $76- $67= $9.00

Less interest expense= -$4.02

$6.98

Initial investment= $33.50 (the remaining is provided by borrowing)

Therefore holding period return= 20.84% =6.98/33.5

c. Compute the holding period return (including the information from part b) if the investor pays a commission of $0.40 per share on both the purchase and sale transaction.

Amount borrowed=$67/2= $33.50

Interest @ 12% = $4.02 =0.12x33.5

Dividend income = 4 x $0.50= $2.00

Capital gains= $76- $67= $9.00

Less commision= 2 x $0.40 -$0.80

Less interest expense= -$4.02

$6.18

Initial investment= $33.50 (the remaining is provided by borrowing)

Therefore holding period return= 18.45% =6.18/33.5

3. You open a margin account with a brokerage firm. The initial margin requirement is ...

#### Solution Summary

Answer to 9 Investment Fundamentals and Portfolio Management questions dealing with return on stock, holding-period return on investment, margin account, market price per share, value of stock, expected return of the portfolio, beta of the portfolio, CAPM, value of options at expiration.

Investment Fundamentals

Please see the attached file.

1. John Smith has been reviewing the stock of ABC. John has estimated that the stock will have the following possible returns and probabilities:

Return Probability

-0.15 0.10

-0.05 0.20

0.05 0.35

0.15 0.25

0.25 0.10

a. Compute the expected return on ABC stock.

b. Compute the standard deviation of returns on ABC.

2. A stock sells for $67 per share and pays a quarterly dividend of $0.50. One year later, the stock sells for $76.

a. Compute the holding-period return on this investment.

b. Compute the holding period return assuming that the investor could buy this stock borrowing half of the purchase price at 12 percent per annum interest.

c. Compute the holding period return (including the information from part b) if the investor pays a commission of $0.40 per share on both the purchase and sale transaction.

3. You open a margin account with a brokerage firm. The initial margin requirement is 50 percent, and the maintenance margin requirement is 25 percent. You purchase 100 shares of a stock selling for $40 per share.

a. How much money do you need to have in your margin account to make this purchase? (Ignore commissions.)

b. What is the amount of your margin loan from the broker?

c. If the stock falls to $32, what is the margin in the account?

d. At what stock price will you receive a margin call?

4. What is the market price per share of Whopie, Inc. if the firm had net income of $200,000, earnings per share of $2.70, total equity of $800,000, and a market to book value ratio of 1.5?

5. The companies in the electrical parts industry have an average earnings multiple of 16. John's Parts, Inc. manufactures electrical parts, and you have forecast that the company will earn $3.60 per share and its stock will sell at the industry average multiple 3 years from now. Estimate the value of John's Parts stock in 3 years. If the required rate of return is 14 percent, what is the present value of John's Parts stock?

6. Tom Jones has identified the following securities for a portfolio:

Security Amount Invested Expected Return Beta

A $25,000 0.05 1.4

B $35,000 0.11 0.1

C $5,000 0.15 0.5

D $35,000 0.01 1.9

Compute the expected return of the portfolio. Compute the beta of the portfolio.

7. The Elvis Alive Corporation, makers of Elvis memorabilia, has a beta of 2.35. The return on the market portfolio is 13%, and the risk-free rate is 7%. According to CAPM, what is the risk premium on a stock with a beta of 1.0?

8. Discuss the 3 forms of market efficiency and the evidence for each form of market efficiency.

Three forms of efficiency

Three forms of market efficiency have been identified, which are as follows:

1 The weak form

This form of efficiency reflects the situation where share prices follow a 'random walk'. By this we mean that prices move up or down on a random basis without regard to what has happened in the previous days. In other words, there is no predictable pattern in share price movements, and so we cannot look at past price movements to help us predict future share prices. The weak form of efficiency suggests that current share prices fully reflect any information contained within past share prices.

There are some investors who try to identify patterns occurring in share price movements (which is known as technical analysis). However, this type of analysis will not be profitable for investors in a capital market that has weak form efficiency. They will be wasting their time as there are no predictable patterns to detect.

2 Semi-strong form

The semi-strong form extends the notion of efficiency a little further and describes the situation where any published information relating to a company will be reflected in its share price. This means that investors who spend time poring over company annual reports, company announcements, industry trends, economic forecasts and so on (which is known as fundamental analysis) would not be able to make superior returns on a consistent basis. They will be wasting their time as this information has already been incorporated into the share price.

3 Strong-form

This form of efficiency is the ultimate form of efficiency in the sense that it describes the situation where all relevant information, whether it is within the public domain or whether it is outside the public domain, will be reflected in the price of a share. This means that even access to 'inside' information such as management decisions or intentions, would not enable investors to make superior returns on a consistent basis.

These different forms of market efficiency represent a form of progression. Thus, a market that is efficient in the semi-strong form will also incorporate the features of the weak form (that is, random share price movements). A market that is efficient in the strong form will incorporate the features of the semi-strong form (rapid and unbiased price adjustment to published information) and will also incorporate the features of the weak form (random price movements). Thus, it would not be possible for a market to be efficient in the strong form but not incorporate the features of the semi-strong and weak forms.

Market evidence

You may wonder what evidence is available to support these various forms of efficiency. The evidence supporting the existence of the weak form of efficiency is really overwhelming. Tests have been conducted in many countries over many time periods and the results almost always point to the existence of a random pattern of share prices. The evidence supporting the existence of semi-strong form of efficiency is less overwhelming, but nevertheless very convincing, at least for the major world stock markets. Tests of the semi-strong form have often involved an examination of price movements following the release of new information, such as profit announcements, and the results have usually shown that share prices re-adjust quickly and accurately to the new information. This implies, of course, that investors cannot make abnormal gains by reacting quickly to any new information.

Tests of the strong form have often involved an examination of the performance of investment fund managers. These fund managers are assumed to have access to a wide range of information, not all of which is in the public domain. The results show that despite this apparent advantage over private investors, fund managers are unable to generate consistently superior performance over time. However, the existence of the strong form of efficiency in major capital markets is a more contentious issue than the existence of the other two forms.

What are the lessons to be learned?

Having identified the various forms of market efficiency and the evidence in support of each form, we need to be clear what the implications are for the managers of a business. It can be argued that there are really four key lessons that should be learned.

9. Compute the value of the following options at expiration:

a. An IBM July 90 call when IBM sells for $98

b. An Eastman Kodak April 25 call with the stock priced at $19

c. A Wall-Mart January 60 put with Wal-Mart stock selling for $48

d. A Pfizer October 35 put with the stock priced at $42.

10. Define a futures contract and explain the process of daily resettlement with futures prices.

View Full Posting Details