In this clip from the CFA Level I Orientation, William A. Trent, director of the exam development division at the CFA Institute, offers 10 essential strategies that every student should follow when preparing for CFA exams. Though Trent warns students that earning a CFA can be a difficult process–with the global pass rate averaging only 40% for the June 2010 exam–he noted that "more and more CFA designation is held in high regard by employers."

|

• 
• 
• 
• 
• 
• 

A reader left me a comment and suggested this interesting video about Ken Griffin.

Ken founded Citadel at the age of 22 with $4.2m. He started two funds from his dorm room at Harvard, and he claims that in between classes he would make trades. His first 'seeder' was Frank Meyer of Glenwood Capital who was amazed at Ken's success and his ROI. Frank provided $1m for Ken to invest while Ken was only 19, and the result exceeded his expectation.

Here is a video on Opalesque.tv in which Frank Meyer describes the keys of seeding new managers, as he did with Ken.

|

• 
• 
• 
• 
• 
• 

Morgan Stanley Questions you must prepare for

|

• 
• 
• 
• 
• 
• 

Goldman Sachs Interview Skills _Must see Video

|

• 
• 
• 
• 
• 
• 

|

• 
• 
• 
• 
• 
• 

|

• 
• 
• 
• 
• 
• 

AIM: Relate the difference between true and risk-neutral probabilities to interest rate drift.

42.1 Assume a binomial interest rate tree where the six-month rate either jumps up 50 basis points or jumps down 50 basis points. The real-world (or “true”) probabilities are 50% and 50% for each up- and down-state. If the interest rate drift is +20 basis point under risk-neutral probabilities, what is the risk-neutral probability of an up-state (p)?

* a. 50%
* b. 60%
* c. 70%
* d. 80%

42.2 Which of the following is MOST essential to the argument that contingent claims can be valued with risk-neutral pricing?

* a. The no-arbitrage price is invariant to investor risk preferences
* b. The no-arbitrage price accounts for investor risk preferences
* c. Investors are risk-neutral in the imaginary world
* d. The discount rate impounds investor risk aversion

42.3 In regard to the valuation of contingent claims (derivatives) by risk-neutral pricing, each of the following is true EXCEPT for:

* a. Expected discounted value will equal arbitrage price
* b. We must assume the growth (return) on the underlying equals the risk-free rate
* c. The risk-free discount rate is appropriate
* d. The derivative price is the same in the imaginary world (risk-neutral investors) and the real world

Answers:

|

• 
• 
• 
• 
• 
• 

Business Graph
AIMS: Using replicating portfolios develop and use an arbitrage argument to price a call option on a zero-coupon security. In addition: Explain why the option cannot be properly priced using expected discounted values. Explain the role of up-state and down-state probabilities in the option valuation.
Questions:

40.1 Assume the market six-month and one-year spot rates are 2.0% and 2.2%, respectively. Assume, per Tuckman’s two-step binomial interest rate tree (i.e., each step is six months), that the six months from now the six-month rate will be either 2.5% (+0.5%) or 2.0% (-0.5%) with equal probability. If a bond’s face value is $1,000, what is the market price of the bond (note: Tuckman assumes semi-annual compounding)?

* a. $968.45
* b. $964.63
* c. $978.36
* d. $982.12

40.2 What are the risk-neutral probabilities?

* a. p = 90.1% and 1-p = 9.9%
* b. p = 9.9% and 1-p = 90.1%
* c. p = 80.1% and 1-p = 19.9%
* d. p = 19.9% and 1-p = 80.1%

40.3 Use a replicating portfolio to determine the price of a call option, that matures in six months, to purchase the $1,000 face value bond at a strike price of $990. What is the market price of the call option?

* a. $0.25
* b. $1.25
* c. $3.25
* d. $9.25

40.4 What is the discounted expected value of the call option?

* a. $0.97
* b. $1.27
* c. $1.97
* d. $2.37

Answers:

|

• 
• 
• 
• 
• 
• 

This question is time-consuming (it just took me two hours to write it) but I hope it gives practice to the notoriously difficult risk-neutral idea in Tuckman. I think if you do each step, you cannot help but confront the idea. I still have to re-read the section on risk-neutral, after years and already several reviews; and I only feel I grasp it barely. Very difficult idea - David H

AIM: Define risk-neutral pricing and explain how it is used in option pricing.
Questions:

41.1 Assume a two-step one-year binomial interest rate tree (each step is six months) used to price a one-year zero coupon bond. In six months, at the first step (when the bond has a six month maturity), the bond price will be either $978 in the up-state or $982.80 in the down-state. The REAL-WORLD probabilities that correspond are 50% (up) and 50% (down). The bond has a face value of $1,000 and, since this is Tuckman, we assume semi-annual compound frequency.

What are, respectively, the down- and up-states of the INTEREST RATES at forward six months (node 1 if today is node 0)?

* a. 3.0% and 4.0%
* b. 3.5% and 4.5%
* c. 4.0% and 5.0%
* d. 4.5% and 5.5%

41.2 Assuming the up- and down-states are symmetrically +0.5% and -0.5% from the current six month rate, what is the bond’s expected discounted expected?

* a. $968.72
* b. $969.12
* c. $960.23
* d. $961.17

41.3 If the one-year spot rate is 4.1%, what is the bond’s (expected) market price?

* a. $968.72
* b. $969.12
* c. $960.23
* d. $961.17

41.4 If p is the probability of an up jump to the up-state and (1-p) is the probability of a down jump to the down-state, what are, respectively, the up- and down-jump RISK-NEUTRAL probabilities?

* a. 70.1% (p) and 29.9% (1-p)
* b. 29.9% and 70.1%
* c. 80.1% and 19.9%
* d. 19.9% and 80.1%

41.5 Assume a call option on this bond (i.e., option to purchase the $1,000 face value bond) has a strike price $980.00. What is the expected discounted value of the call option?

* a. $0.82
* b. $1.02
* c. $1.17
* d. $1.37

41.6 For the same call option, what is the actual (market) price of the option?

* a. $0.82
* b. $1.02
* c. $1.17
* d. $1.37

41.7 What is the implied drift in the interest rate?

* a. -30 basis point
* b. -20 basis points
* c. +20 basis points
* d. +30 basis points

41.8 Which of the following best describes risk-neutral pricing?

* a. Risk-neutral probabilities as inputs into expected discounted valued
* b. Real world probabilities as inputs into expected discounted valued
* c. Risk-neutral probabilities but only in the imaginary world of risk aversion
* d. Risk-neutral probabilities replace the risk-free rate to incorporate risk aversion

Answers:

* Here in forum


[Learn] Tax argument for risk management L1.T1.41 [practice, foundation]

Posted: 03 Aug 2010 11:12 AM PDT

Time To Pay

AIM: Explain how risk management can create value moving income across time and reducing taxes
Questions:

41.1 Assume Stulz’ stylized firm (Pure Gold) that produces one lump-sum, pretax cash flow at the end of a one-year period; i.e., firm value is the discounted present value of the one future cash flow. The riskfree rate is 3%. The firm’s future cash flow is only a function of the the spot price of gold, which is a purely UNSYSTEMATIC market risk. Without hedging, the firm’s future pretax cash flow will be either $0 (low future spot price of gold) or $100,000 (high future spot price of gold). Each outcome is equally likely. The corporate tax schedule of MARGINAL tax rates includes (these are currently accurate):

* 15% of pretax income from $0 to 50,000
* 25% from $50 to $75,000
* 34% from $75 to $100,000

Assume pretax cashflow is identical to pretax income. If the firm hedges the price risk of gold, by how much does this risk management increase firm value?

* a. Zero, per the Hedging Irrelevance Theorem
* b. $3,520
* c. $4,520
* d. $5,520

41.2 What does it mean for, instead, shareholders to practice a homemade hedge in this situation. And would that create value?

* a. Short gold futures, yes
* b. Short gold futures, no
* c. Long gold futures, yes
* d. Long gold futures, no

41.3 Which of the following is the necessary assumption that makes validity Stulz’ “tax argument for risk management” (the assertion that risk management can add value where taxes are concerned)?

* a. Tax carryforwards
* b. Tax shield
* c. Personal taxes
* d. Differential tax rates

Answers:

|

• 
• 
• 
• 
• 
•