Homework 1

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Christopher Smaldone
Principles of Investments
Homework 1:
Chapter 3: Question 3,4,5,6,7,8,9,10,12,15,18,19,20,21.
3. The market where the new issues are offered to the public for the first time is considered a
primary market. The market where the shares which are already being issued in the primary market
are traded is a secondary market.
4. well the clients may be an individual form, or a company. The security dealers also buy and
sell security for their own purpose. They operate on the stock exchange and provide some
structure for training proposes. However, the earn profit by capturing momentum and spread
between bid and ask rates as well.
5. Private placements are most likely to be used by the public because they avoid cost and time
which is suffered in preparation of the public issue. In addition, they are mostly offered to few
institutional investors and are held until maturity.
6. stop loss orders are classified into two types, namely buy stop-loss orders and sell stop-loss
orders. Market orders will be executed during market hours. Market order allows you to buy or
sell a security at the prevailing market price. Limit sell order instructs the broker to trade a
certain number of shares at that exact time
7. it has declined because there is an increase in high frequency trading programs in 1000 or 200
share lot. Its made it difficult to maintain a position with just a single purchase.
8. Underwriters give advice on how to sell securities. They purchase securities from corporations
in bulk and sell to public. Prospectus contains information about the company’s financial
position, market image, profitability in shares, and securities they are issuing.
9. Purchasing on margin is a kind of loan or leverage or debt that the investor takes from a broke.
Margin trade allows an investor to purchase more stock than he or she can actually buy from
their own funds. The upside potential and downside of an investment portfolio is overstated by
margin trades because it shows profit or loss. A rise or fall in price of security will lead to gain or
loss for an investor. The gain or loss is much higher percentage than the actual investment. The
investor has bought the security combining own and borrowed fund.
10. Price uncertainty but not execution uncertainty.
12. a. there is not limit of the losses as potential losses can increase in price of IBM.
b. maximum loss is determined on the collateral and willingness to meet the money
requirements when the margin calls are coming.
15. a. the margin is 66.7%. $8,000/$12,000 = 66.67
b. the share value is $9,000 (30 x 300). But she also borrowed $4,000 at the rate of 8%.
Therefore, her liability is $4,320 ($4,000 x 1.08). her margin is $4,680 ($9,000-$4,320)
the margin ratio is 52%. However, she will not receive any margin call
c. -41.5%. $4,680 - $8,000 / $8,000 = -41.5
18. a. $10,000/$50 – 200 shares. Investor bought 200 shares.
If stock goes up 10%, the new value of the investment would be $10,000 x 1.10 =
$11,000. When investor borrows $5,000 at 8 % per year you would do $5,000 x 1.08, which
equals $5,400. By selling off the stock, you would take $11,000 - $5,400 to get $5,600. As you
calculate the rate of return, you would take $5,600 -$5,000/$5,000.. $600/$5,000 = 12%
b. Value of stock – loan amount/value of stock
.30 x (200 x P) = (200 x P)- $5,000
140 x P =$5,000
$5,000/140 = $35.71
19. a. shorts sales
Initial investment - $2500
Beginning price of share - $50
Number of shares short sold - $100
Ending price of share - $55
Dividends per share – 0
Initial margin % - 50%
Maintenance margin % - 30
Return on short sale
Gain or loss on share = -50
Dividends paid – 0
Net income =-500
Return on investment = -20%
Margin positions – 36.36%
Price for margin call – 57.69
20. a stop loss is an order under which the transaction gets triggered automatically as soon as the
price of the stock reaches the price mentioned. However, it will sell out the security as soon as
the price falls and reaches the mentioned price so that the loss can be restricted.
A US based investor owed a few stocks of M corporation. $67.95 is the current price of the
stock and the ask price is $68.05. Basically, it means he wants to ask the brother to sell the stock
as soon as the stock price reaches $68. The security can be sold at $67.95 and the investor has
ordered the broker to sell as soon as the price reaches $68 which means also means it actually
falls below. The investor gave a stop loss order because he wanted to limit his losses just in case
the price dropped. All in al, the price has fell below the limit.
21. a. 55.50 (ask price)
b. 55.25 (bid price)
c. Trade will not be executed
d. trade will be executed
Chapter 5: Question 1, 2, 3,4,5,6.
1. Since the fifth percentile value of risk is -30% and the first percentile value at risk of a
portfolio needs to be estimated, the percentile of return decreases, so does the return, the
first percentile value at risk will earn less than the fifth percentile value of risk (VaR).
2. In a sharpe ratio, the expected rate of return on portfolio is calculated based on the
arithmetic average. Geometric average is more useful in the case of series where events
are dependent, and it proves better in the case of series where events are independent. In
case of different portfolios, returns will be independent of each other.
Geometric average uses effects of compounding and may mislead the result.
3. When the estimate for sharpe measure is done, if the average excess real return that
accounts for inflation is used then the ratio calculated will not be appropriate. The reason
being is because all the items in this measure are calculated using nominal figures. The
inputs used should also be nominal data only.
4. Decrease. To return to the proper risk return relationship the portfolio will need to
decrease the amount of risk free investments.
5. Mean = [.3 x 44] + [.4 x 14] + [.3 +(-16)]
(13.2 +5.6 – 4.8)
= 14 %
Standard deviation = [.3x(44-14)^2] +[.4x(14-14)^2+[.3x(-16-14)^2]
270+ 270 = 540
6. A. The holding period for boom = 30% (50-40+2/40)
The holding period for normal economy is 10% = (43-40+1/40)
The holding period for recession is 13.75% = (34-40 +.50/40)
Standard deviation: (.33x30%) + (.33x10%) +(.33x-13.75%)
.33[30-8.75]^2 + .33[10-8.75]^2 +.33[-13.75-8.75]^2
150.52 + .5208 +168.75 = 319.79. the square root of that is 17.88% is standard
deviation
b. expected holding period returns on portfolio invested in business adventures and half
in treasury bills comes out to be 6.375% = (.5=8.75%+.5x4%) -> 4.375% +2% =6.375
The standard deviation is 8.94%-> (.5 x17.88%)
Chapter 6: Question 1, 2, 3, 4, 13,18
1. If correlation coefficient is below 1 it would result in greater diversification. It
provides a gain due to imperfect returns on component securities. The standard
deviation would be smaller than the securities weighted average standard deviations.
2. The covariance with the other assets is more important because diversification is
accomplished with correlation with the other assets. in addition, it helps determine
that exact number.
3. A and B will have the same impact of increasing the Sharpe ratio for .40 to .45.
4. If you allocate the same amount of money between risky portfolios and risk-free
assets like T-bills, it will change the expected return on overall portfolio. Therefore, it
will result in changing the first term present in the numerator of sharpe ratio that is
expected on the portfolio. If you change the expected return on the portfolio it also
changes the sharpe ratio as well which is extremely important to know.
5. A. The variance of stock A when residual standard deviation and beta remain the
same at .18
(1.5)^2 x (.2)^2 +(.3)^2
(2.25x.04) +.09
.09+.09 = .18
The variance of stock A with a beta of 1.65 is .1989
(1.65)^2 x(.2)^2+(.3)^2
=(2.7225 x.04) +.09
.1089 +.09 = .1989
In addition, if you do (1.5)^2 x (.2)^2 +(.33)^2
= (2.25x.04) +.1089.. .09 +.1089 = .1989
B. in both cases, the stock variance will be increased from .18 to 0.1989
6. A. the expected mean return and the variance of the stock fund seems to be more than
the values computed in the spreadsheet 6.2. If you look at the values, the range is high in
terms of the variance in the new values provided in the question. But, its less in the
values computed in that spreadsheet.
B. the mean return is 11.20%, the variance is 445.860, it is more than the mean return of
10%, and the variance is 347.10. the intuition in part A is correct.
C. the new covariance is -85.6, and the values given in the spreadsheet 6.4 is -74.8. The
correlation between stocks and bonds is the same at -0.49. the covariance is increased in
the new values of stock returns. However, the covariance increased because the stock
returns are more extreme in the recession and boom periods.
Chapter 7:
Question 3,4, 5, 6, 7, 9, 13,14,15,16, 17, 18, 19, 21, 23.
3. a. false. If the beta is zero, then the CAPM predicts that the expected rate of return on the stock
will be equal to the risk-free rate
b. true – the higher the beta value of a security is, the higher the expected return the investor require
to hold the security.
c. False – the beta of a portfolio is calculated by the weighted average of al the betas of the securities
in a portfolio. The beta of the market portfolio is 1 and the beta of a risk-free asset is 0. The beta of a
portfolio with 75% invested in the risk-free asset and 25% invested in the market portfolio has a beta of .25
4. For company discount store, you would 4% +1.5 [6%] -> 4% +9% = 13%
For company everything, 4% +1 [6%] -> 4%+6% =10%
5 . Discount store = $1.50/(.11 - .05) = $25.00. the stock price of $1 discount store is $21.43
and the stock price of Everything $5 is $25.
$1.50/(.10 -.05) = $30.00. the stock price of $1 discount store is $18.75
The stock price of $1 Discount store should be $18.75, but its market price is $21.43. therefore,
the stock is over priced.
The stock price of Everything $5 should be $30 but its market price is $25. Therefore, the stock
is underpriced.
6. 15%
7. Option A
9 . 15%/10% = 1.5
15. possible. According to CAPM, expected rata takes into account only systematic risk, which
is measured by beta and not for total risk that is measured by standard deviation. Since the beta
values are not give, the portfolio return can be based on standard deviation given
13. not possible. Port A has a higher beta than Port. B. the two portfolios cannot exist in
equilibrium.
14. possible. The CAPM is valid, the expected rate of return compensates only for systematic
risk. Port. A’s lower rate of return can be paired with a higher standard deviation, as long as
A’s beta is less than B’s
16. not possible. Since port. A has a higher expected return than the market with a lower
variance.
16. possible. Port A plots below the CML, as any asset is expected to.
17. not possible. 10 + [1.5 x (18-10)] = 22%. The expected return for Portfolio A is 16%. That
is portfolio A plots below the SML ( -6%) . the portfolio is over priced.
19. Possible. Scenario is not inconsistent with the CAPM
18. not possible. The required return is 17%, which is greater than 16%. It’s a negative alpha.
21. .18 x 100 = P -$91
$18 +$91 = $109
23. .06 = .08 + beta (.18 - .08)
.06 = .08 + beta (.10)
Beta (.10) = .06 - .08
Beta (.10) = -.02 .. the beta would be -.2
Chapter13:
Question 4, 5,6,9,10,14, 15, 19.
4. $1.20/1.0850 + $1.44/1.1772 + $33.33/1.1772 = $.92 + $1.22 + $28.31 = $30.45 -> intrinsic value
5. 1.22 x (1 +.05)/32.03 +.05
.04 +.05 = 9% -> required rate of return is 9%
6 . 1.05/32.03 + .05 -> .0327 +.05 = .082%.. 8.2%
9 . .6 x .10 =.06
The P/E ratio = 100/5 = 50
10.
14. $2.10/11% = $19
15. .05 +1.5 (.10 -.05)
.05 +.075
.125 0r 12.5 % is the required rate of return
$2.5/.125 -.04
$2.5
.085= $29.41 is the high-flyer stock
19. a. $1.00/.12-.-8 = $25.00
b. $25(1.08)3 = $31.49
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