Question 1
Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. a. What is the price of the option if it is a European call? b. What is the price of the option if it is an American call? c. What is the price of the option if it is a European put? d. Verify that put–call parity holds.

Question 2
Assume that the stock in Question 1is due to go ex-dividend in 1.5 months. The expected dividend is 50 cents. a. What is the price of the option if it is a European call? b. What is the price of the option if it is a European put? c. Use the results in the Appendix to this chapter to determine whether there are any circumstances under which the option is exercised early.

Question 3
What is the price of a European put option on a non-dividend-paying stock when the stock price is $69, the strike price is $70, the risk-free interest rate is 5% per annum, the volatility is 35% per annum, and the time to maturity is six months?

Question 4
A foreign currency is currently worth $1.50. The domestic and foreign risk-free interest rates are 5% and 9%, respectively. Calculate a lower bound for the value of a six-month call option on the currency with a strike price of $1.40 if it is (a) European and (b) American.

Question 5
Consider a stock index currently standing at 250. The dividend yield on the index is 4% per annum, and the risk-free rate is 6% per annum. A three-month European call option on the index with a strike price of 245 is currently worth $10. What is the value of a three-month put option on the index with a strike price of 245?

Question 6
An index currently stands at 696 and has a volatility of 30% per annum. The risk-free rate of interest is 7% per annum and the index provides a dividend yield of 4% per annum. Calculate the value of a...

...How can risk influence risk premium? How are risk and return related?
Risk and return are the fundamental basis upon which investors make their decision whether or not they should invest in a particular investment. How they are related and the influence between the two, is the decision making process that all investors must weigh up. This essay will show how risk can influence risk premium, outlining their relationship and how risk and return are related.
Within any investment there is a certain amount of risk, which must be taken into account by an investor when deciding to invest. Risk is defined as the chance of financial loss or, more formally the variability of returns associated with a given asset. (Gitman, et al., 2011, p. 208) This concept in finance is the idea that all investment carries a risk, the higher the risk, the greater the return, however the adverse is also relevant, when the risk of an investment is lower the return is expected to also be lower. However, with all investment there is never a guarantee of return.
Return is the total gain or loss experienced on an investment over a given period of time. It is measured by the asset’s cash distributions plus change in value, divided by its beginning-of-period value. (Gitman, et al., 2011, p. 208) Returns on investment are the motivation...

...isolation may have little, or even no risk if held in a well-diversified portfolio.
b. The feasible, or attainable, set represents all portfolios that can be constructed from a given set of stocks. This set is only efficient for part of its combinations.
c. An efficient portfolio is that portfolio which provides the highest expected return for any degree of risk. Alternatively, the efficient portfolio is that which provides the lowest degree ofrisk for any expected return.
d. The efficient frontier is the set of efficient portfolios out of the full set of potential portfolios. On a graph, the efficient frontier constitutes the boundary line of the set of potential portfolios.
e. An indifference curve is the risk/return trade-off function for a particular investor and reflects that investor's attitude toward risk. The indifference curve specifies an investor's required rate of return for a given level of risk. The greater the slope of the indifference curve, the greater is the investor's risk aversion.
f. The optimal portfolio for an investor is the point at which the efficient set of portfolios--the efficient frontier--is just tangent to the investor's indifference curve. This point marks the highest level of satisfaction an investor can attain given the set of potential portfolios.
g. The Capital Asset Pricing Model (CAPM) is a general...

...P8-17 Total, Nondiversifiable and Diversifiable Risk
c) Because Diversifiable risk can be eliminated through portfolio diversification, the more relevant risk is the Nondiversifiable risk. This kind of risk can be attributed to market forces and factors that affect ALL the firms and cannot be eliminated through portfolio diversification. In this case, the nondiversifiable risk is about 6.00%. Notice that the area between the red curve and the green line (which represents the diversifiable risk) diminishes as it approaches the green line.
P8-18 Graphical Derivation of Beta
c) Looking at the graph we can see that the best-fit line of returns for Asset B is steeper (has greater slope) than Asset A
The slopes of these lines are the betas for each asset: 2.61 for Asset B and 1.48 for Asset A. The greater beta value of Asset B signifies that it is more responsive to market factors and therefore makes it more risky than Asset A.
P8-20 Interpreting Beta
a. A 15% increase in market return would lead to an 18% (15% x 1.20) increase in the asset’s return.
b. An 8% decrease in market return would lead to a 9.6% (8% x 1.20) decrease in the asset’s return.
c. If the market return doesn’t change, the asset’s return more or else stays the same holding other things constant.
d. This asset has a beta of 1.20 signifying that it is 1.2x more responsive...

...at t=0 (before the first film is released) rather than at t=1?
3. Assuming a discount rate of 12% (riskfreerate of 6% and a risk premium of 6%) calculate the NPV for all the sequels. Use the expected negative costs and the expected revenues given in Table 7.
4. Using the “decision-tree” approach, calculate the per-movie value of the sequel rights to the entire portfolio of 99 movies released in 1989 by the six major studios.
5. Assume that a maximum of ten sequels can be made in any given year. Using the same decision-tree approach, what would you estimate to be the per-movie value of the sequel rights to the entire portfolio of 99 movies released in 1989 by the six major studios?
6. Using the Black-Scholes approach, calculate the per-movie value of the sequel rights to the entire portfolio of 99 movies released in 1989 by the six major studios. (Assume once again that there is no maximum to the number of sequels that can be made in a given year). You must provide details of how you estimated the inputs to the B-S formula.
a. Asset value
b. Exercise price
c. Volatility of asset returns
d. Time to maturity
e. Risk-freerate
HINT: Note that the time to maturity of the options is when uncertainty is resolved not necessarily when the sequel is made. The asset value is what...

...RISK & RETURN
TOPIC 4
Learning Objectives
1. Understand the meaning of risk and return
2. Identify risk and return relationship
3. Discuss the measurement of expected return
and standard deviation
4. Understand portfolio and diversification
5. Distinguish the different types of investment
risks
6. Measurement of return based on CAPM
WRMAS
2
RETURN DEFINED
• Return represents the total gain or loss on an investment.
•
Basic concept:
Each investor desires a return for every single dollar of their
investment.
Example 1:
Rita invests in 10 unit shares valued at RM1000. At the end of
year, she sells all the shares @ RM1100. How much return
received by Rita for her investment?
RM100 (Holding return dollar gain)
r = RM1,100 + 0 – RM1,000
RM1,000
= 10% (so holding period rate of return is 10%)
WRMAS
3
Return Defined
Exercise 1
Calculate the holding period rate of return of each
quarter below.
1st Quarter
2nd Quarter
3rd Quarter
4th Quarter
Dividend
0.50
1.20
0
1.95
Purchase price
100
98
101
102
Selling Price
98
101
102
108
HP Rate of
Return
?
?
?
?
WRMAS
4
EXPECTED RETURN
• Expected Return ( r )- the return that an investor expects to
earn on an asset, given its price, growth potential, etc.
• Required Return ( r )- the return that an investor requires...

...Risk and Return -II
PGDM/MMS- SEM-II
PROF. V. RAMACHANDRAN
FACULTY- SIESCOMS , NERUL
1
PORTFOLIOS & RISK
What is an Investment Portfolio
A group of Assets that is owned by an
Investor
Single Security is riskier than Investing in a
Portfolio.
Portfolio may contain- Equity Capital, Bonds ,
Real Estate, Savings Accounts, Bullion,
Collectibles etc.
In other words the Investor does not put all
his eggs in to one Basket.
2
Diversification –Risk Reduction
Let us assume you put your money equally into the
stocks of two companies Banlight Limited, a
manufacturer of sunglasses and Varsha Limited, a
manufacturer of rain coats.
If the monsoons are above average in a particular
year, the earnings of Varsha Limited would be up
leading to an increase in its share price and
returns to shareholders.
On the other hand, the earnings of Banlight would
be on the decline, leading to a corresponding decline
in the share prices and investor's returns.
If there is a prolonged summer the situation would
3
be just the opposite.
Diversification –Risk Reduction
While the return on each individual stock might
vary quite a bit depending on the weather but the
return on your portfolio (50% Banlight and 50%
Varsha stocks) could be quite stable because the
decline in one will be offset by the increase in the
other. In fact, at least in theory, the offsetting could
eliminate your risk entirely.
The table...

...%, commas, etc.). Enter all dollars without decimals and all interestrates in percentage with up to two decimals. Read the syllabus for examples.The points for each question are listed in parentheses at the start of the question, and the total points for the entire assignment adds up to 100.
In accordance with the Coursera Honor Code, I (Shravan Vepa) certify that the answers here are my own work. Thank you!
Question 1
(5 points) In a world with no frictions (i.e., taxes, etc.), having debt is always better because it increases the value of the firm/project.
False.
True.
Question 2
(5 points) The return on equity is equal to the return on assets of a project/firm.
Always true.
Never true.
Sometimes true.
Question 3
(10 points) Moogle, Inc. is in the same business as Google, Inc., but has recently retired all its debt to become an all-equity firm. Its return on equity has dropped from 12.25% to 10.60% as a result of this. Google, Inc. continues to have debt in its capital structure, and its debt-to-equity ratio is 30%. What is the return on assets of Google, Inc.(No more than two decimals in the percentage interestrate, but do not enter the % sign.)
Answer for Question 3
Question 4
(10 points) Suppose CAPM holds, and the beta of the equity of your company is 2.00. The expected market risk premium (the difference between the expected market return and the...

...percentage interestrate, but do not enter the % sign.)
Answer for Question 3
Question 4
(10 points) Suppose CAPM holds, and the beta of the equity of your company is 2.00. The expected market risk premium (the difference between the expected market return and the risk-freerate) is 4.5% and the risk-freerate is 3.00%. Suppose the debt-to-equity ratio of your company is 20% and the market believes that the beta of your debt is 0.20. What is return on assets of your business? (No more than two decimals in the percentage interestrate, but do not enter the % sign.)
Answer for Question 4
Question 5
(10 points) You are planning on opening a consulting firm. You have projected yearly cash flows of $2 million starting next year (t = 1) with a growth rate of 3% over the foreseeable future thereafter. This endeavor will require a substantial investment and you will have to convince investors to provide you the capital to do so. You will invest some of your own money, convincing other investors will of course be useful for your valuing your own investment decision. A critical piece of your analysis is figuring out the present value of the cash flows of the business. Your research has revealed the following information: similar consulting businesses equity has an average beta of 2.40 and the average...

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