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Management of Financial Institutions > Risk Management MFI > Flashcards

Risk Management MFI Flashcards

1
Q

How does interest rate risk arise for banks?

A

Interest rate risk arises from the basic nature of standard banks’ business model (getting deposits and turning these into loans). Deposits are short-term, while loans are long-term, which means that on the balance sheet of banks, there is a maturity mismatch of assets and non-equity liabilities (= there is a duration)

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2
Q

How does market risk arise?

A

Market risk originates from changes in market values of instruments in a bank’s trading book.

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3
Q

What is a bank’s trading book?

A

The trading book comprises securities that the bank will not hold to maturity but is continuously and actively traded for profit speculation. In particular, this trading book consists of a bundle of different assets.

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4
Q

What is amortization of a loan?

A

Amortization means that the payments made to the banks after receiving a loan are used to cover part of the principal. If a loan is non-amortizing, the principal is paid back in full at maturity

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5
Q

How is Duration of a loan/bond calculated?

A

Step 1: multiply the PV of each payment by the period in which the payment occurs: PV_t*t

Step 2: Sum the PV_t*t of all payments (=numerator of duration), and divide by the PV of total CFs connected to the loan/bond

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6
Q

Given following information, calculate the duration of the loan:

PV of CF_t:1/2=52,830.19
PV of CF_t:1=47,169.81

A

52,830.191/2=26,415.1
47,169.811=47,169.81
Sum=73,584.91

D=73,584.91/(52,830.19+47,169.81) = 0.7358

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7
Q

Holding everything else constant, how will an increase in YTM affect the Duration of a Bond with annual coupon payments?

A

Increasing YTM will decrease the duration of the bond, since it decreases the PV of the bond payments (= bond price), leading to a smaller amount in the duration calculation nominator of the duration formula.

Intuition:
As the yield to maturity increases, the higher yields discount later cash flows more heavily and
the relative importance, or weights, of those later CFs decline when compared with earlier CFs on the bond.

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8
Q

In what value range can a coupon-bond duration lie?

A

By construction, the duration of coupon bonds will be above 0, but lower than N (maturity of the bond)

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9
Q

The duration of zero-coupon bonds is by construct equal to…?

And how is the duration of a zero-coupon bond affected by changes in YTM?

A

The duration of a zero-coupon bond equals its maturity:
D(zero-coupon bond) = N

Any change in YTM will have no effect on the duration since it will always be equal to N

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10
Q

Assume two coupon bonds with the only difference being maturity. How will a change in YTM affect the pricing of these two bonds? Why is it relevant whether the bond trades at par?

A

Longer maturities affect coupon-bond prices positively (since a larger number of coupon payments will be received by the bondholder), but only until YTM=Coupon (bond is at par). Beyond this point, maturity affects the bond price negatively because the large amount (face value) to be repaid at maturity is discounted more heavily for a long-maturity bond compared to a short-maturity bond (page 13 in notes).

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11
Q

Assume two bonds with different coupon rates, which are obviously priced differently with the largest coupon bond being most expensive. As YTM increases, the relative difference in the pricing of these bonds decreases - the development is convex. Why?

A

The price differences are convex as YTM increases (the relative difference between bond prices decrease). This is because the higher the discount rate, (YTM) the lower the future value of the bond cash flow, and the lower the relative difference between CFs of bonds with higher and lower YTM (page 12 in notes).

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12
Q

What is the relationship between MATURITY of a bond and Duration? (positive or negative)

A

Positive: as maturity increases, the Duration also increases - i.e., the interest rate risk increases with maturity

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13
Q

What is the relationship between Duration and coupon rate of a bond? (Positive or negative)

A

Negative: As coupon rate (coupon interest payment) of a bond increases, the duration decreases.

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14
Q

What is Dollar Duration and how does it differ from (regular) Duration?

A

Dollar duration is the dollar value change in the price of a security to a one percent change in the return on the security.
(Regular) Duration is a measure of the percentage change in the price of a security for a one percent change in the return on the security.

The dollar duration is intuitively appealing in that we multiply the dollar duration by the change in the interest rate to get the actual dollar change in the value of a security to a change in interest rates.

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15
Q

Assume an 11-year, $1000 bond paying a 10% semi-annual coupon and at par. The duration is 6.763 years. What are the modified duration and the dollar duration?

A 
MD(semiannual) = D/1+(R/2)
MD(semiannual) = 6.763/(1+(0.1/2)=6.441

Dollar duration = MDP
Dollar duration = 6.4411000=6441

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16
Q

For a bond with a dollar duration of 6,441, how will the price ($1000) change, given an interest rate increase of 0.1%?

A

Using the dollar duration, we can derive the change in an asset price given change in interest rate by:

Change in price = - Dollar duration*Change in Interest Rate

Change in price = - 6,441*0.001= -$6.441

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17
Q

For a bond with a dollar duration of 6,441, how will the price ($1000) change, given an interest rate decrease of 0.2%?

A

Using the dollar duration, we can derive the change in an asset price given change in interest rate by:

Change in price = - Dollar duration*Change in Interest Rate.

Change in price = - 6,441*-0.002= $12.882

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18
Q

What is the formula for Modified Duration and Dollar Duration?

A

MD (semi annual) = D/(1+(R/2)

Dollar Duration = MD * P(:price of the asset)

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19
Q

Estimation of bond price given a change in YTM using dollar duration typically deviates from actual bond prices (NPV method). How will this error differentiate in terms of the size of interest rate change?

A

With a larger interest rate shock (change), the error of the estimation will be larger as compared to when the interest rate change is smaller.

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20
Q

How is Leverage-Adjusted Duration Gap calculated?

A

Leverage-Adjusted Duration Gap = (Duration_asset - Duration_liability)*(D/D+E)

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21
Q

Suppose a bank has an asset with a duration of 9.94 and liability with a duration of 1.8975. The value of the asset is 1,000,000, and is financed by equity and 900,000 debt. What is the leverage-adjusted duration gap?

A

Leverage-Adjusted Duration Gap = (Duration_asset - Duration_liability)*(D/D+E)

Leverage-Adjusted Duration Gap = (9.94-1.8975)*(900,000/1,000,000) = 8.23225 Years

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22
Q

How is the change in equity value from a change in interest rate calculated?

A

Change in Equity Value = -((Duration of asset - Duration of liability)(D/E))Asset Value*(Change in interest rate/1+Old Interest Rate)

23
Q

How is RELATIVE change in interest rate calculated?

A

Relative Change in Interest Rate = Change in interest rate/(1+(Old interest rate/payment frequency PA)

E.g., for semi-annual payments, the relative change in interest rate is:
Relative Change in Interest Rate = Change in interest rate/(1+(Old interest rate/2)

24
Q

Which (leverage-adjusted) duration gap is preferred in the following scenarios:
-If interest rate development is uncertain
-If rates will certainly increase
-If rates will certainly decrease
Why?

A
  • If interest rate development is uncertain: zero-(leverage-adjusted) duration gap
  • If rates will certainly increase: Negative (leverage-adjusted) duration gap
  • If rates will certainly decrease: Positive (leverage-adjusted) duration gap

By doing so, the financial institution will only experience an increase (or no change) in equity value in the event of change of interest rate.

25
Q

How is the duration for a portfolio of assets calculated?

A

For each asset value (reported on B/S), we multiply this with the specific duration of the asset. Doing this for all assets in the portfolio, summing the products and divide it by the total value of assets (reported on B/S), we get the duration of assets in a portfolio:

D_A(:portfolio)=(A_1(D_1)+…+A_n(D_n))/Total Value of Assets

26
Q

How is the duration for a portfolio of leverage calculated?

A

For each debt(liability-side) type (reported on B/S), we multiply this with the specific duration of the liability. Doing this for all sources of debt in the portfolio, summing the products and dividing it by the total value of debt (reported on B/S: Liabilities-equity), we get the duration of leverage in a portfolio:

D_L(:portfolio)=(L_1(D_1)+…+L_n(D_n))/Liabilities-Equity

27
Q

How is the Average Duration of a portfolio of assets and a portfolio of liabilities calculated respectively?

A

Average Duration of Assets=(A(D_A )+B(D_B )+⋯+N(D_N ))/(Total value of assets)

Average Duration of Assets=(A(D_A )+B(D_B )+⋯+N(D_N ))/(Total value of Liabilities - Equity)

28
Q

How is the percentage change in the price calculated after a change in the interest rate?
Calculate the percentage price change in a bond with P=1,108.144 and P(after change)=1,070.345

A

ΔP = (PV_Bond Post Change - PV_Bond Pre Change) / (PV_Bond Pre Change)

29
Q

Everything else equal, will a change in interest rate affect bond price most if the interest rate increases or decreases?

A

Due to the convex relationship between Price and YTM, an increase in YTM results in a smaller price decline than the price gain associated with a decrease of equal magnitude in YTM;

Bond price increase more significantly than it decreases given the same amount of inverse interest rate change.

30
Q

Given an increase of 0.1% in interest rate, duration of 12.1608, the convexity of 212.4, the price of the bond being $1000, the initial interest rate of 8%, what is the estimated change in bond price?

A

A better approximation of the change in price can be obtained by correcting the duration model with the convexity adjustment:

∆P=(-D∆R/((1+R) ))P+1/2*CX(ΔR)^2

Plugging in the information:
∆P=(-12.16080.001/((1+08) ))1000+1/2*212.4(0.001)^2=-$11.15

This, we can conclude that with the convexity adjustment, we arrive at a change in the price of the bond of -$11.15 given the increase in the interest rate of 0.1%

31
Q

How is convexity calculated?

A

CX = 1/P(1+R/M)^2SUM(PVt*(t+1/M))

32
Q

How to calculate maximum adverse interest rate change with 99%confidence?

A

Max_(Adverse Change) with Conf=0.99)= 2.33σ

33
Q

How to calculate maximum adverse interest rate change with 95%confidence?

A

Max_(Adverse Change) with Conf=0.95)= 1.65σ

34
Q

How is price volatility calculated?

A

Price Volatility = MD * Max_(Adverse Change with Conf=0.99 or 0.95)

35
Q

How is DEAR calculated?

A

DEAR = $Market Value of Position * Price Volatility

36
Q

How can DEAR be adjusted to account for potential losses over multiple days?

Calculate the VAR for a bond for a 10-day period assuming DEAR = $13,065

A

The DEAR can be adjusted to account for losses over multiple days using the formula: Nday VAR = DEAR*[N]^½
, where N is the number of days over which potential loss is estimated.

Nday VAR = 13,065 * [10]^½ = $41,315

37
Q

Explain the relationship between maturity and interest rate sensitivity for bonds

A

Prices for long maturities bonds are more sensitive to interest rate changes than those of short maturities

38
Q

Following is NOT true about bond duration:

A) Measures the relative maturity of a bond

B) Duration decreases with coupon rate

C) Duration usually (except for deep discount bonds, c &laquo_space;R) increases with maturity, but at a decreasing rate

D) Duration decreases with YTM

A

A) Measures the relative maturity of a bond = WRONG

Duration is a measure of the EFFECTIVE maturity of a bond. Duration is a weighted average of CF payment dates, where the weights are proportional to the PV of each CF. That is, we take the payment dates, and weight them by the relative importance of each payment in terms of PV.

39
Q

Explain the relationship between coupon rate and interest rate sensitivity for bonds

A

Prices for high coupon bonds are less sensitive to interest rate changes than those of low coupon

40
Q

Why is immunization a dynamic strategy?

A

If a FI has managed to achieve a zero-duration gap, it has achieved perfect immunization. However, as soon as YTM (market interest rate) changes, this will change the PV and thus the duration of a bond, leading to the occurrence of a duration gap. Thus, the FI must reimmunize to maintain a zero D gap.

41
Q

Why is the price change estimated using the duration model said to be pessimistic?

A

The duration model underpredicts the bond price increase (when rates decrease) and overpredicts the bond price decrease (when rates increase). Hence, it is pessimistic!

42
Q

What happens to the accuracy of the duration model price change estimation as the magnitude of interest shock increases?

A

The error in the duration model gets larger with larger interest rate shocks

43
Q

Why is an amortizing bond less risky for the bond holder than a regular straight bond?

A

An amortizing bond is often less risky because there is a lower risk that the issuer will default on the entire face value at maturity since portions of the face value are repaid on specific dates during the lifetime of the bond.

44
Q

Assume that the standard deviation of a bond over the last years 15 bps, and assume the yield changes are normally distributed.

A. What is the highest yield change expected if a 99 percent confidence limit is required?

B. What is the highest yield change expected if a 95 percent confidence limit is required?

A

A. Highest yield change given a 99% confidence interval =
standard deviation2.33 -> 152.33bp=34.95bp = 0.3495%

B. Highest yield change given a 95% confidence interval =
standard deviation1.65 -> 151.65bp=24.75bp -> 0.2475%

45
Q

Calculate Daily Earnings at Risk from a given Position from Adverse Moves in FX Markets with 99% confidence:

  • FX: $1.6m
  • $/€: 1.25
  • St. Dev: 62.5bp
A

To calculate the DEAR, we need following two inputs:
(i) Market Value Position & (ii) Price (Exchange Rate) Volatility:

Step 1: Calculate the Dollar-Equivalent Market Value of Position:
MV of position = FX($ per €) = $1.6m*1.25=$2m

Step 2: Calculate the Exchange Rate Volatility:
Volatility = St. Dev2.33 = 0.006252.33 = 0.0145625

Step 3: Calculate the DEAR:
DEAR = Market Value of Position * Volatility = $2m*0.0145625 = $29,125

46
Q

What is the difference between VAR and Expected Shortfall (ES) as measures of market risk?

A

VAR corresponds to a specific point of loss on the probability distribution. It does not provide
information about the potential size of the loss that exceeds it, i.e., VAR completely ignores the
patterns and the severity of the losses in the extreme tail.

Expected shortfall (ES) is a measure of market risk that estimates the expected
value of losses BEYOND a given confidence level, i.e., it is the average of VARs beyond a given
confidence level. ES, which incorporates points to the left of VAR, is larger when the probability
distribution exhibits fat tail losses. Accordingly, ES provides more information about possible
market risk losses than VAR.

For situations in which probability distributions exhibit fat tail
losses, VAR may look relatively small, but ES may be very large.

47
Q

What is a Spot Contracts?

What is a Future/ Forward Contract?

A

SPOT CONTRACT is an exchange of cash, or immediate payment, for financial assets, or any other
type of assets, at the time the agreement to transact business is made, i.e., at time 0.

FUTURES & FORWARD CONTRACT are agreements between a buyer and a seller at time 0 to exchange the asset for cash (or some other type of payment) at a later time in the future. The specific grade and quantity of asset is identified at time 0, as is the specific price paid and time the transaction will eventually occur.

48
Q

What does it mean to be short in futures contracts?

What does it mean to be long in futures contracts?

A

To be SHORT in futures contracts means that you have agreed to sell the underlying asset at a future time

To be LONG means that you have agreed to buy the asset at a later time.

In each case, the price and the time of the future transaction are agreed upon when the contracts are initially negotiated.

49
Q

What is the difference between futures and forwards?

A

Futures: Exchange-traded over-the-counter contracts that are standardized.

Forward: Negotated and tailored to satisfy the needs of the parties entering the contract. Here, you have greater counter-party risk than in a futures contract.

50
Q

How is the profit/loss of a buyer of a forward contract at maturity calculated?

A

Profit (Buyer of Forward) =Bond Market Value at Maturity - Price of forward

51
Q

How is the profit/loss of a buyer of a forward contract at maturity calculated?

A

At maturity, the buyer of a forward makes a profit of:

Profit (Buyer of Forward) =Bond Market Value at Maturity - Price of forward

52
Q

How is the profit/loss of a seller of a forward contract at maturity calculated?

A

At maturity, the seller of a forward makes a profit of:

Profit (Seller of Forward) = Price of forward - Bond market value

53
Q

In reality, we have transaction cost, which means that you cannot in reality continuously rebalance and maintain a zero-duration gap, since it would be very costly. Thus, in practice, the manager must determine how costly and often this exercise is (perhaps with quarterly frequency).

A
54
Q

In reality, perfect immunization through duration gap elimination on a frequent basis by dynamic rebalancing is recommended for banks.

TRUE/ FALSE

A

Theoretically - yes
Practically - no
In practice, we have transaction cost, which means that you cannot in reality continuously rebalance and maintain a zero-duration gap, since it would be very costly. Thus, in practice, the manager must determine whether the cost of dynamic rebalancing is too high relative to the benefit of duration gap elimination (perhaps with quarterly frequency is more appropriate).

Management of Financial Institutions (7 decks)

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