Financial Risk Manager

Loss Given Default Chapter 4 Servigney

2008-07-18T13:48:02-08:00

Hi David,

Can you explain the meaning of creditor’s run and debt cushion and also figure 4.2 ?

Thanks
Sipani

Market A - Question 8

2008-05-05T11:49:20-08:00

Question:

In regard to exotic options:

(i) If c = value of a European call option, what is the value of the same but where it is a forward start option?
(ii) If we increase the frequency of observing the asset price, what happens to the value of a lookback call? What happens to the value of a barrier option?
(iii) Warren Buffet has argued that executive stock options ought to be indexed to the Standard and Poor’s 500 index, instead of striking with a fixed exercise price (since the owner of such an option profits from even riskless appreciation in the stock)? Which exotic valuation can be used for this sort of indexed stock option?

Answer:

(i) The value is c. For a non-dividend paying stock, the value of a forward start is the same as the value of a regular at-the-money option with the same life as the forward.

(ii) The lookback becomes more valuable as we have more chances to observe a lower minimum. Regarding the barrier, it DEPENDS on the type of barrier option. More frequency = greater chance of triggering the barrier: a knock-out goes DOWN in value, but an knock-in goes UP in value.

(iii) This is tantamount to an EXCHANGE option because the exercise is indexed to another asset (the S&P;500 index). As such, it can be valued by a variant of the Black-Scholes called the Margrabe. (Hull 6th Edition, p 540).

Market A - Question 4

2008-05-05T11:07:09-08:00

Question:

A bank enters an interest rate swap on a notional of $100 million. The bank will receive a fixed rate of 5% per annum (semiannual compounding) and pay 6-month LIBOR. The swap has a remaining life of 15 months. The LIBOR curve is not shifting over time: the 3 month LIBOR = 3%, 6-month = 3.5%, 9-month = 4.0%, and 15-month = 5%.

(i) What is the value of the swap?
(ii) Alternatively, the bank considered a loan of $100 million. Is the expected loss (swap vs. loan) the same?
(iii) In this swap transaction, what is an example of CREDIT risk?
(iv) What is an example of MARKET risk?

Answer:

(i)
Look at this spreadsheet for the calculations.

We can treat as two bonds or two FRAs. If we treat the swap as two bonds, we have a fixed-rate bond and a floating-rate bond.

The fixed rate bond is the sum of the PV of its cash flows (an FRM candidates needs to know how to do this calculation.):

($2.5 MM )EXP[(-3%)(-0.25 years)] = $2.48 ;i.e., the PV of the first swap ("coupon") payment
($2.5 MM )EXP[(-4%)(-0.75 years)] = $2.43 ;i.e., the PV of the second swap ("coupon") payment
($102.5 MM )EXP[(-5%)(-1.25 years)] = $96.29 ;i.e., the PV of the third swap ("coupon") payment plus the notional

The floating rate bond only needs to PV a single cash flow that has two parts:
1. the first floating swap plus
2. the notional because, in this case, in three months at the moment the first swap payment is made on the floater, the fair value of this floating leg is exactly equal to the notional (= par value)! Why? future “coupons” are paid at the same rate they will be discounted.

(ii)
No, the exposures are entirely different.
The entire loan is exposed (the full amount can be lost).
In the case of an interest rate swap, the bank does not have exposure on the notional amount as the principal is not exchanged.
The bank’s credit risk is only to the extent the swap, from the bank’s perspective, is positive.
To illustrate, it is possible the bank never has credit risk! The swap could theoretically have negative value to the bank for the tenor of the swap.

(iii)
Counterparty risk is the class of credit risk that matters here: the risk the counterparty will default on the swap
(again, this is only relevant where the swap has positive value to the bank. Negative value = no [instantaneous] credit risk)

(iv)
Market risk, in the case, would refer to interest rate changes that impact the value of the swap. Notice that credit risk, in this case, is institution-specific (the counterparty) and market risk is a systemic factor.

Market A - Question 2

2008-05-05T11:05:33-08:00

Question:

Assume the Standard and Poor’s Index currently stands at 1400; the dividend yield on the index is 2%; and the riskless rate is 4%.

(i) What is the price of the four-month futures contract?
(ii) Is this contango or backwardation?
(iii) Tough: Do we expect normal contango or normal backwardation?

Answer:

(i) The “universal” cost of carry formula above will handle most situations (if the costs/benefits can be expressed as constant %). Costs of carry are: r = riskless rate, u = storage costs. Benefits of carry are: q = income/dividend, y = convenience yield.

In this case, F(0) = (1400)EXP[(4%-2%)(4/12)] = about 1409

(ii)
Contago because F > S

(iii)
First, we don’t know with certainty. “Normal backwardation” is possible with “contango.” “Normal contango” is possible with “contango.” I don’t know is a good answer!

Second, see p 121 of Hull. Where there is positive correlation btwn asset (stock) and underlying (S and P), we expect forward price to understate the expected future spot. As here, where systemic risk exists, we can expect normal backwardation (consistent with traditional theory, somewhat empirically verified, that normal backwardation ought to be the state of things because speculators [i.e., those taking a long position in the futures contract] demand compensation in the form of a risk premium). So, for both those reasons, we could *expect* or theorize normal backwardation.

BT IS A GREAT BUY!

2008-08-27T05:07:56-08:00

Hi David,

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It is not only that your answers are fast but also the quality of your explanations is superb. I know that it takes time to understand our questions and to elaborate concise but comprehensive explanations that are easy to understand. I do appreciate your support and time.

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Kind regards,

Relationship between Forward and Futures Prices

2008-08-25T11:28:07-08:00

Hi David,

Regarding the relationship between forward & futures prices (pg. 19) which is also addressed in Treasury bonds Futures & Eurodollar Futures (page 26), I would appreciate it if you could please clarify the following:

1) Both Eurdollar futures and T-bills are quoted in price (as opposed to FRA). As rates increase, prices fall. Therefore the long position on either a ED or T-bill future loses money as rates increase. Is this correct?

2) Eurodollar futures contracts are based on 90-day LIBOR, which is an “add-on” yield. What is an “add-on” yield? I assume that a 30-day Eurodollar futures contract is a 30-days futures contract on 90-day LIBOR. Is this correct?

3) How do we calculate the price of a ED futures contract (given the futures quoted price, Z)?

Contract price = $10,000*[100-(100-Z)*(0.25)].

I don’t quite undertand this formula (where does it come from? notional is 1 million). How can I relate it to LIBOR? I mean the relationship between Z and LIBOR.

4) Fixed income values fall when interest rates rise, so rates and values are negatively correlated. Because of the mark-to-market feature of futures, when bond prices fall and funds are needed (margin call), borrowing costs are higher (interest rates). And when funds are generated (bond prices increase providing an excess margin), the reinvestment rate is lower. Therefore, since the correlation between bond prices and interest rates is negative, futures < forwards (pg. 19). I don’t understand why the implied rate on the futures contract will be greater than the rate on the FRA. What am I missing?

Thanks

VAR Mapping

2008-08-26T21:20:27-08:00

Hi David,

Didn’t get the logic behind mapping to EUR Spot in Forward foriegn currency contract screencast. I mean why did u choose k12*j12?

Anil

OpRisk C - Question 1 (Basel II Credit)

2008-08-24T19:24:13-08:00

Question:

In the Standardized Approach to Credit Risk in the Basel II Accord, what is the regulatory capital charge for:

(i) $10 million AA rated corporate loan
(ii) Euro 100 million C rated corporate loan
(iii) $15 million UNRATED bank loan
(iv) AU 12 million AAA sovereign obligation

Answer:

If you would like to view a dynamic spreadsheet of the standardized grid, please refer to this EditGrid/XLS worksheet..
In that XLS, you can input the exposure type and the rating, and the risk weight is returned.

(i) AA rated corporate loan has a risk weight of 20%. Risk weighted assets (RWA) = 20% * $10 MM = $2 MM. Capital charge = 8% * $2 MM = $160,000. In summary, ($10 MM)(20%)(8%) = $160,000

(ii) C rated corporate loan has a risk weight of 150%. Risk weighted assets (RWA) = 150% * Euro 100 MM = Euro 150 MM. Capital charge = 8% * Euro 150 MM = Euro 12 MM. In summary, (Euro 150 MM)(150%)(8%) = Euro 12 MM

(iii) An unrated bank loan has a risk weight of 50% (or 100%). Risk weighted assets (RWA) = 50% * $15 MM = $7.5 MM. Capital charge = 8% * $7.5 MM = $600,000. In summary, ($15 MM)(50%)(8%) = $600,000

The alternative (Bank option #2) assigns the bank a risk weight based on the rating of the bank’s country.

(iv) AAA rated sovereign has a 0% risk weight. So the capital charge is zero.

OpRisk B - Question 4 (Case studies)

2008-08-10T19:50:24-08:00

Question:

For each of the following, try to name the single most significant risk factor and, similarly, try to identify the single alternative measure that might have prevented losses (operational or otherwise).

(i) Metallgesellschaft
(ii) Sumitomo
(iii) Long-Term Capital Management (LTCM)
(iv) Barings Bank

Answer:

Note: unlike an exam questions, this question allows for some subjectivity. There is not necessarily a single correct answer in each case.

(i) In regard to the single risk factor for the Metallgesellschaft case, arguably it starts with BASIS RISK. The stack-and-roll strategy entailed hedging short positions in long-term forward contracts with long positions in short-term forward contracts. The oil curve shifted from backwardation to contango. Most of the others problems resulted from this. Accounting forced mark-to-market losses on the hedges (without offset gains on the underlying), which in turn triggered margin calls and a funding liquidity crisis (although the large positions also exhibited MARKET liquidity risk). Please note: in the case of Metallgesellschaft, there was no fraud.

It is hard to exactly name a single preventative measure. The case says, “it seems that management was directly responsible for the financial catastrophe. If managers had not taken such a large position in long futures, or if they had at least used put options as a hedge for their position, then the magnitude of the cash flow problem could have been reduced.”

(ii) In the case of Sumitomo, Hamanaka was cornering the copper market in a plan of “outright fraud and illegal trading practice.”
The key preventative measure was “proper internal control measures as well as better portfolio diversification to protect against downside risk.” The lack of internal control included: lack of management supervision, lack of risk management, and failure to control the market.

(iii) “The event trigger for the LTCM crisis was MODEL risk.” In particular, LTCM’s risk management model “relied too heavily on the bell-shaped normal distribution curve” and their signature trade “known as equity volatility, comes straight from the Black-Scholes model. It is based on the assumption of constant volatility.”

In regard to prevention at LTCM, one could make several different arguments. But arguably the key measure would have been more comprehensive and rigorous STRESS TESTING (rather than their leaning on “theoretical models"); e.g, stress testing changes in market risk with greater volume, stress testing credit risk scenarios.

(iv) Leeson is the classic “rogue trader” so, not totally unlike Sumitomo, the key cause is an OPERATIONAL RISK factor; i.e., “the regulatory, supervisory, and corporate governance framework failed completely.” The preventions concern better internal risk controls; i.e., standards for traders, better information systems, separation of settlement/trading, and management oversight.

Clarification in Credit Risk

2008-08-26T00:03:41-08:00

Hi David...Request you to please clarify the following -

1) In Merton Model, one of the practical difficulty which hampers the empirical relevance of the Merton Model is “The estimation of asset volatility is difficult due to the low frequency of observation” - Pls. explain this statement.

2) In Chp.3 of De Servigny in KMV Model it says - “The estimation of the firm value process is also difficult: How should we estimate the drift and volatility of the asset value process when this value is unobservable.” - Cud you pls. explain this.

3) In Chpt.4 of De Servigny in regard to paper by Frye (2000a, 2000b), it says that PD&LGD;are negatively correlated. Shouldn’t it be PD & Recovery Rate instead?

Pls. help.

Regards
Sipani