Questions and Answers of Investment Risk Management

A perpetual option is one that never expires. (Such an option must be of American style.) Use Exercise 6 to show that the value of a perpetual call on a non-dividend-paying stock is $C=S$.Data from
Consider a deterministic cash flow stream $\left(x_{0}, x_{1}, x_{2}, \ldots, x_{n}\right)$ with all positive flows. Let $\mathrm{PV}(r)$ denote the present value of this stream at an interest
There are two propositions:(a) I flip a coin. If it is heads, you are paid \$3; if it is tails, you are paid $\$ 0$. It costs you $\$ 1$ to participate in this proposition. You may do so at any
A New York firm is offering a new financial instrument called a "happy call." It has a payoff function at time $T$ equal to $\max (.5 S, S-K)$, where $S$ is the price of a stock and $K$ is a
It is August 6. You are the president of a small electronics company. The company has some cash reserves that will not be needed for about 3 months, but interest rates are very low. Your chief
If the Simplico mine is solved with all parameters remaining the same except that $u=1.2$ is changed to $u=1.3$, the value of the lease remains unchanged to within three decimal places. Indeed,
A stock has volatility $\sigma=.30$ and a current value of $\$ 36$. An American put option on this stock has a strike price of $\$ 40$, and expiration is in 5 months. The interest rate is \(8
Suppose that the price received for gold extracted from time $k$ to $k+1$ is the average of the price of gold at these two times; that is, $\left(g_{k}+g_{k+1}\right) / 2$.However, costs are
Consider the stock of Examples 14.3 and 14.4, which has $\sigma=.20$ and an initial price of $\$ 62$. The interest rate is $10 \%$, compounded monthly. Consider a 5-month option with a strike
You are considering an investment in a tree farm. Trees grow each year by the following factors:The price of lumber follows a binomial lattice with $u=1.20$ and $d=9$. The interest rate is
There is a market for bets on the outcome of a coin toss. The possible outcomes are heads, tails, and edge. There are three assets traded in that market:Asset A pays $\$ 1$ independent of the
Consider the stock and bond lattices on the left of Figure 14.18. Each has unit cost of $\$ 1$ with the payoffs shown at the end nodes. There is a new asset available-a derivative of the first two
A derivative security of European style with expiration in 1 year has this payoff: $\max (0, \min (3 K-S, S-K))$, where $K=10$ is the strike price and $S$ is the price of the underlying stock
The cumulative normal distribution can be approximated (to within about six decimal places) by the modified polynomial relationwhereUse this formula to find the value of a call option with parameters
Consider a perpetual American put option (with $T=\infty$ ). For small stock prices it will be advantageous to exercise the put. Let $G$ be the largest such stock price. The time-independent
Traders in major financial institutions use the Black-Scholes formula in a backward fashion to infer other traders' estimates of $\sigma$ from option prices. In fact, traders frequently quote
Using the same parameters as in Example 15.2. find the value of the 5-month call if the initial value of the stock is $\$ 63$. Hence estimate the quantity $\Delta=\triangle C / \Delta S$.
Gavin Jones believes that for a derivative security with price $P(S)$. the values of $\triangle, \Gamma$, and $\Theta$ are related. Show that in fact +SA+ = rP.
Show that for a European call or put on a non-dividend-paying stock = N' (d1) SoT SN' (d) -Ke-T N(d2). 2T
Assume we have a non-dividend-paying stock governed by the stochastic differential equation $\mathrm{d} S_{t}=\mu S_{t} \mathrm{~d} t+\sigma S_{t} \mathrm{~d} z_{t}$ and a risk-free asset carrying
A marketed asset's price $x$ is governed by the mean reverting processwhere $\eta, \theta$, and $\sigma$ are positive constants and $z$ is a Wiener process.(a) Let $V(x, t)$ be a given
For a derivative of an asset that follows standard geometric Brownian motion, it may be useful to find the sensitivity of the derivative price with respect to a parameter of the underlying process.
As with Exercise 10, the sensitivity of a derivative asset with respect to the underlying interest rate $r$ is termed rho and defined asFor a call option on stock following the Black-Scholes
Great Western Bank has offered a special certificate of deposit (CD) tied to the S\&P 500.Funds are deposited into the account at the beginning of a month and are held in the account for 3 years.
Suppose that it is desired to estimate the expected value of a random variable $x$. (This random variable might be the discounted terminal value of a call option on a stock that is following a
Use the control variate method of Exercise 13 to determine the value of a 5 -month Asian call option on a stock with $S_{0}=\$ 62, \sigma=20 \%$, and $r=10 \%$ and a strike price of $\$ 60$.(a)
Pay-later options are options for which the buyer is not required to pay the premium up front (i.e., at the time that the contract is entered into). At expiration, the holder of a pay-later option
Suppose you buy a new home and finance $90 \%$ of the price with a mortgage from a bank. Suppose that a few years later the value of your home falls below your mortgage balance and you decide to
Solve Exercise 16 in Chapter 14 assuming that the annual storage cost of cut lumber is $5 \%$ of its value.Data from Exercises 16 chapter 14 You are considering an investment in a tree farm. Trees
Find the value of the put for Mr. Smith described in Example 15.9. Example 15.9 (A foreign currency put) Mr. Smith, a successful but cautious U.S. businessman, has sold a product to a Japanese firm,
An investor has utility function $U(x)=x^{1 / 4}$ for salary. He has a new job offer which pays $\$ 80,000$ with a bonus. The bonus will be $\$ 0, \$ 10,000, \$ 20,000$, $\$ 30,000, \$ 40,000, \$
Suppose an investor has exponential utility function $U(x)=$ $-e^{-a x}$ and an initial wealth level of $W$. The investor is faced with an opportunity to invest an amount $w \leq W$ and obtain a
Suppose $U(x)$ is a utility function with Arrow-Pratt risk aversion coefficient $a(x)$. Let $V(x)=c+b U(x)$. What is the risk aversion coefficient of $V$ ?
The Arrow-Pratt relative risk aversion coefficient is\[\mu(x)=\frac{x U^{\prime \prime}(x)}{U^{\prime}(x)} .\]Show that the utility functions $U(x)=\ln x$ and $U(x)=\gamma x^{\gamma}$ have constant
The HARA (for hyperbolic absolute risk aversion) class of utility functions is defined by\[U(x)=\frac{1-\gamma}{\gamma}\left(\frac{a x}{1-\gamma}+b\right)^{\gamma}, \quad b>0\]The functions are
A venture capitalist with a utility function $$U(x)=\sqrt{x}$$ carried out the procedure of Example 11.3. Find an analytical expression for $$C$$ as a function of $$e$,$ and for $$e$$ as a
There is a useful approximation to the certainty equivalent that is easy to derive. A second-order expansion near $\bar{x}=\mathrm{E}(x)$ gives\[U(x) \approx
An investor with unit wealth maximizes the expected value of the utility function $U(x)=a x-b x^{2} / 2$ and obtains a mean-variance efficient portfolio. A friend of his with wealth $W$ and the same
Suppose an investor has utility function $U$. There are $n$ risky assets with rates of return $r_{i}, i=1,2, \ldots, n$, and one risk-free asset with rate of return $r_{f}$. The investor has initial
The promoter of the film venture offers a new investment designed to attract reluctant investors. One unit of this new investment has a payoff of three times the original investment if the venture is
Explain that in a CAPM framework, the projection price of a new asset is a universal zero-level price for all mean-variance investors.
A market is partially complete if for any $m$ in the market and any real function $f$, then $f(m)$ is also in the market. In addition, there are other assets that are not traded.As an example,
The following is a general result from matrix theory: Let $\mathbf{A}$ be an $m \times n$ matrix. Suppose that the equation $\mathbf{A x}=\mathbf{p}$ can achieve no $\mathbf{p} \geq \mathbf{0}$
Suppose an investor uses the quadratic utility function $U(x)=$ $x-\frac{1}{2} c x^{2}$. Suppose there are $n$ risky assets and one risk-free asset with total return $R$. Let $R_{M}$ be the total
At the horse races one Saturday afternoon Gavin Jones studies the racing form and concludes that the horse No Arbitrage has a $25 %$ chance to win and is posted at 4 to 1 odds. (For every dollar
We can transform the log-optimal pricing formula into a risk-neutral pricing equation. From the log-optimal pricing equation we have\[P=\mathrm{E}\left(\frac{d}{R^{*}}\right)\]where $R^{*}$ is the
Identify the benefits of BCM that are easy to quantify and those that are not easy to quantify.
Identify the initial and ongoing expenses related to the BCM program.
Once completed, why would a BCP ever change?
Define the three stages in the BCM cycle.
Why are comprehensive checklists and questionnaires beneficial during the site inspection and management interview process?
Why should senior management rather than IT managers have final approval over the IT Disaster Recovery Plan?
Identify reasons why quick decisions are often needed during the initial stages of a crisis event.
What are the significant differences between the responsibilities of the CMT and the ERT?
What are the characteristics of a person who would be a good leader during a disaster?
Does the BCM Coordinator need to be an employee at the senior management level?
Why are all important operations not considered to be critical operations?
Identify reasons why an operation with a short RTO will require a more expensive BCM than a similar operation but with a longer RTO.
Identify the one time and recurring costs that should be examined to determine the total cost of a strategy.
Consider facility, personnel and IT resources. In general, all the resource components identified above are necessary for most organizations. Can you think of organizations that can operate without
Identify the business continuity problems associated with the following types of crisis events:a. Community-wide crisis events.b. Crisis events that provide no warning.c. Crisis events that destroy
Identify and discuss strategies that are effective for hurricanes but ineffective for earthquakes.
Identify strategies that can introduce inefficiencies to a manufacturer in times of normal operations.
Identify the logistical problems associated with using a local IT alternate site location in a heavily fortified buildings during a major community-wide crisis event.
Identify the logistical problems associated with using a distant IT alternate site location during a major community-wide crisis event.
If a good IT alternate site plan is in place, why is it important to have a data center recovery plan for the main data center?
Identify the environmental benefits of electronic data over hardcopy data.
Identify three examples of IT threats for each of the following exposures: disclosure, modification and destruction.
Choose an auditing instance concerning the physical security of an IT center and develop a brief control objective and an auditing objective for it.
You have just conducted a site visit to a data center and discovered that the main entrance had a card key entry system installed as a security feature. Unfortunately, the system was inoperable so
Discuss why it might be impractical to have all operating systems in business rated for the equivalent of military trusted systems.
Discuss why the role of a database administrator in any large organization has both political and technical dimensions
Discuss the salient issues in permitting employees in business organizations access to social networking sites.
If an organization has subcontracted threat monitoring services, does the organization need to review the actual actions being taken by the subcontractor?
Identify key earthquake mitigation steps.
Identify key hurricane mitigation steps.
List the most common ‘social distancing policies’ that can be used in the workplace if a pandemic outbreak occurs.
List the most common ‘personal protection equipment’ that can be used in the workplace if a pandemic outbreak occurs.
An intercom message is received stating that a hostile intruder situation exists in the building and that a shelterin-the place should be performed. Subsequently, a fire alarm is heard indicating the
What types of crisis events provide a warning period?
Discuss ways an organization can interface with civil responders without making a substantial financial commitment.
What other advantages can BCM gain from partnering with EMAs, NGOs and other business continuity professionals?
What BCM activities crossover among two or more phases or emergency management?
What other activities in one phase affect activities in another?
What other emergency preparedness skills might the company already have on hand either through existing relationships, employee involvement or through corporate involvement in the community?
In addition to RA and BIA, what other information is found both in BCPs and CEMPs?
Besides the American Red Cross what other charitable organizations have a mission that spans across all four phases of emergency management?
Is there a VOAD in your community? How is it organized? What agencies are members? What agencies in the community are not members?
What trade associations, educational groups or networking groups for business continuity professionals exist in the area? Do they have student membership or allow new members to attend a free session?
What conferences are coming up that could provide value to BCM?
What other online forums have you found to be valuable?
What other educational resources exist for business continuity practitioners?
In addition to utility and insurance companies, what other businesses that already support companies – outside the supply chain – need to be included in BCM coordination with external agencies?
What are examples in the news of coordination between emergency management, NGOs and the private sector? What is the nature of these relationships and their involvement through the four phases of
Is there a clear point in time when emergency response ends and business continuity begins?
What additional information could a comprehensive damage assessment provide that was not available in the preliminary damage assessment?
Why should department responsibilities be assigned on an enterprise-wide basis?
Are there any advantages of holding a conference with the media immediately after a crisis strike before all the facts are known?
Satellite phones, intercom systems and two-way radios are three communication systems used for crisis event warnings or crisis event communication. Is it possible to determine which system is best?
Alerting employees commuting to work about a crisis event at the organization often presents a problem. Identify systems and procedures that can be used to communicate with employees commuting to

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