UNIVERSITY OF CAPE TOWN

SCHOOL OF MANAGEMENT STUDIES

FINANCE 2 FINAL EXAM

BUS3026W

SECTION A: FIXED INCOME INVESTMENTS [45 MARKS]

Question 1                                                                    [16 marks]

A newly issued bond has a coupon rate of 6%, a time to maturity of 15 years and a yield to maturity of 7.5%.

By the end of the first year, the yield to maturity now falls to 6.75%.

If the bond pays coupons annually, calculate the holding period return for a one year investment in such a bond.                                            [3]

Given that capital gains are taxed at 15% and ordinary income at 30%, calculate the after-tax holding period return for the above issue.      [4]

If the bondholder above was very apprehensive with regards to the impact of rising interest rates on the value of his holdings, what feature if agreed to by the issuer could he build into his contract to help limit his interest rate exposure? Explain.                                                                                     [3]

If the bond issuer had similar reservations concerning the rate of decline in interest rates, discuss a value adding feature he/she could build into the contract. [2]

What is BESA? Discuss some of its key functions and primary users.                    [3]

Name one Government Bond Issue listed on BESA.              [1]

Question 2                                                                    [15 marks]

You are given information on the following two bonds on the 1^st of January 2008:

Bond A: Bond B:

Maturity: 18 years Face Value: R1000

Price:                           R1000 Maturity: 18 years

Coupon Rate:                         6% p.a. Coupon Rate: 8.5% p.a.

Payment Dates: 30th Jun/31^st Dec Payment Dates: Quarterly

YTM:                            6% Price: R1000

Explain which one of the following issues has a higher duration?            [2]

If there is a possible change in the YTM of Bond B by 2%, calculate the predicted contribution to the percentage change in price due to duration? [5]

If the convexity of Bond B is 23 and pays coupons semi-annually, calculate the estimated price of Bond A using the Duration-Convexity Rule for a 2% fall in interest rates.                                                               [3]

In light of such an interest rate adjustment in (c) above, will using duration in isolation under- or over-estimate the price change of the bond?             [2]

Compare and contrast one passive versus one active bond management strategy.

Question 3                                                                    [10 marks]

Given the following information on zero-coupon bonds of the defined maturities:

Calculate the implied forward rates                           [3]

Explain the rationale behind the calculation forward rates [3]

TRUE or FALSE (provide a reason for your answer)

Both Expected Short Rates and Forward Rates are directly observable.   [2]

Preferred Habitat can be considered an extension of Liquidity Preference Theory, whereby investors require greater risk premia in order to alter their investment horizons.                                                                       [2]

Expectations Theory and Liquidity Preference Theory are similar in that they both consider all investors to be risk neutral.                    [2]

Question 4                                                                    [4 marks]

Discuss rate anticipation swaps as a bond portfolio management strategy.                    [4]
SECTION B: DERIVATIVE INSTRUMENTS         [45 MARKS]

Question 5                                                                    [35 marks]

Today is 15 October 2008. Mr. DeBondt is an analyst for an investment bank based in Cape Town. Mr. DeBondt's task is to analyse Apex Ltd, a newly listed textile manufacturer on the JSE. Given the dismal global economic outlook, Mr. DeBondt forecasts that the share price of Apex Ltd, currently trading at R50, is expected to move up by 5%, or down by 10% semi-annually. The short-term Treasury bill rate is at 9% per annum.

Use the following option quotations and Mr. DeBondt's forecast to answer the questions below. You are required to show fully-labelled profit/loss graphs in your answer.

OTC European Options on Apex Ltd:

Spot Expiry Strike Call Premium Put Premium

R50 15 Oct 2009 R50 ??? ???

R50 15 Oct 2009 R60 ??? R1,200 (per contract)

Assume the options of Apex Ltd are efficiently priced based on put-call parity, construct a covered call strategy (X = R60) on Apex that expires on 15 October 2009.                                                                             [13]

Assume the options of Apex are efficiently priced based on 2-stage binomial option pricing model, construct a long straddle strategy (X = R50) on Apex Ltd that expires on 15 October 2009.                               [22]

Question 6                                                                    [10 Marks]

It is 15 October 2008. Mr. French holds an equity portfolio consisting of two industrial shares, namely EDCON (5 000 shares) and TELKOM (8 000 shares) respectively. Mr. French's investment analyst, Mr. Fama, has collected the relevant information on these two shares five minutes ago:

Company                    Share Price Beta

EDCON                        R45 0.70

TELKOM                      R55 1.10

Evaluate the value of Mr. French's equity portfolio today. [3]

Compute the Beta of Mr. French's equity portfolio today.                        [3]

Suppose the ALSI futures with closed-out date on 15 Dec 2008 is currently at 21 000. Calculate the number of short futures contracts on ALSI that are required to hedge the Mr. French's equity portfolio. [4

NOTE: Futures Contract Size: Index level x R10

SECTION C: INTERNATIONAL FINANCE           [45 MARKS]

Question 7                                                                    [7 Marks]

(a)    Give one advantage and one disadvantage of the gold standard. [2]

(b)    As an investor, explain the two factors that you would consider before investing in the emerging stock market of a developing country [2]

(c)     Describe the differences between foreign bonds and Eurobonds. Why do most international bonds have high Moody's or Standard & Poor's credit ratings?                [3]

Question 8                                                                    [6 Marks]

Money Tracker, an international money markets specialist, uses the concepts of Purchasing Power Parity (PPP) and the International Fisher Effect (IFE) to forecast spot exchange rates. Money Tracker has gathered the following financial information:

Calculate the following exchange rates (ZAR and GBP refer to the South African and U.K. Pound, respectively):

(a)    The current ZAR spot rate in GBP that would have been forecasted by PPP as at the base period.                                                                                                      [2]

(b)    Using the IFE, the expected ZAR spot rate in GBP one year from now.                    [2]

(c)     Using PPP, the expected ZAR spot rate in GBP three years from now.                      [2]

Question 9                                                                    [6 Marks]

Assume that you are a currency trader, who can enter into transactions with a maximum exposure of $100,000. You see the following quotes on your screen:

What is the maximum profits that you can achieve in $ terms if you undertake a (1) triangular arbitrage, and (2) covered interest arbitrage.                  [6]

Question 10                                                                  [8 Marks]

Heavy Shipping Amalgamated S.A. [HSA], a South African operator purchased a ship from Mitsubishi Heavy Industry. HSA owes Mitsubishi Heavy Industry „100 million in one year. The current spot rate is „15.5/ZAR and the one-year forward rate is „13.75/ZAR. The annual interest rate is 5% in Japan and 8% in South Africa. HSA can also buy a one-year call option on yen at the strike price of ZAR0.0648/„ for a premium of 0.018 cents per „. Assume interest accrues on the premium until the expiry date.

(a)    Compute the future rand costs of meeting this obligation using the money market hedge and the forward hedges.                                                    [2]

(b)    Assuming that the forward exchange rate is the best predictor of the future spot rate, compute the expected future rand cost of meeting this obligation when the option hedge is used.                                                                    [2]

(c)     At what future spot rate do you think HSA may be indifferent between the option and forward hedge?                                                                      [2]

(d)    Explain cross-hedging and discuss the factors determining its effectiveness. [2]

Question 11                                                                  [12 Marks]

The trustees of the Mellon Foundation have solicited input from three consultants concerning the risks and rewards of an allocation to developed international equities. Two of them strongly favour such action, while the third consultant commented as follows:  "The risk reduction benefits of international investing have been significantly overstated. Recent studies relating to the cross-country correlation structure of equity returns during different market phases cast serious doubt on the ability of international investing to reduce risk, especially in situations when risk reduction is needed the most."

Analiza: Activitatea financiara si riscul in cadrul unei organizatii Eseu: Afacerile - comunicare

(a)   Describe the behaviour of cross-country equity return correlations to which the consultants is referring.                                                     [2]

(b)   Explain how that behaviour may diminish the ability of international investing to reduce risk in the short run, making reference to the current financial markets meltdown. [2]

(c)    What factors will influence the correlations among international equity markets in the long run?                                                                                  [2]

(d)   In the recent past, emerging markets have generated higher returns than developed markets. Why do analysts generally expect higher returns from emerging markets? What is the likely impact of including equities from emerging markets in a portfolio solely invested in developed market equities? [3]

(e)   The trustees of Mellon Foundation believe that currency risk will be diversified away in a portfolio of many foreign assets. Should they be concerned if their portfolio now also holds emerging markets' currencies? [3]

Question 12                                                                  [6 Marks]

The table below displays the performance of the constituents of an international portfolio and of its benchmark for the year 2007, with the South African rand (ZAR) as the base currency. During the year, the U.S. dollar appreciated by 10% against the ZAR and the U.K. pound depreciated by 5% against the ZAR.

(a)   What is the excess return of the portfolio compared to the benchmark in the base currency?

(b)   How much of the excess return is attributed to the manager's currency allocation, market allocation and security selection decisions.

SECTION D: RISK MANAGEMENT                    [25 MARKS]

Question 13                                                                  [14 Marks]

As a South African investor, the excessive risk of the current market environment has led you to re-evaluate your investment holdings. You have assessed numerous alternatives from different markets and at present it appears that the New Zealand stock exchange has demonstrated the lowest equity volatility over the recent past.

In order to hedge against potential future losses, you are considering liquidating your current local position and using the proceeds to fund a protective put strategy on the NZX 50 index. You expect that currency volatility will still be significant in coming months and your initial estimates are that the annual mean and standard deviation for the R/$NZ exchange rate will be 13.6% and 23.44% respectively.

You have established that such a portfolio would require an investment of NZ$255,000 in the NZX 50 index with the remainder of your funds to be invested in 50 put options. The contracts are each currently worth NZ$4 375 each, and have a delta of -0.56 to the index. The index level is 2566.5 and the contract multiplier is 10. The dividend yield on the NZX 50 is 1.8%.

The expected weekly return on the NZX 50 is 0.54% while the weekly standard deviation is 2.35%. The 6-month NZ interest rate is 5.77%. The correlation between the R/$NZ and the NZX 50 is 0.23 and the current exchange rate is 5.65 R/$NZ. All dividend yields & interest rates are per annum NACC (continuously compounded).

You have established that a 1-month 99% VaR of 10% relative to your investment value would be acceptable, given your level of risk aversion.

Based on the above information, would your expected position meet your requirements?                                                                                      [14]

Question 14                                                                  [11 Marks]

The following excerpts were taken from an article published on Bloomberg on 28 January.

Excerpt A

"The risk-taking model that emboldened Wall Street to trade with impunity is broken and everyone from Merrill Lynch & Co. Chief Executive Officer John Thain to Morgan Stanley Chief Financial Officer Colm Kelleher is coming to the realization that no algorithm or triple-A rating can substitute for old-fashioned due diligence.

Value at risk, the measure banks use to calculate the maximum their trades can lose each day, failed to detect the scope of the U.S. subprime mortgage market's collapse as it triggered more than $130 billion of losses since June for the biggest securities firms led by Citigroup Inc., Merrill, Morgan Stanley and UBS AG."

Excerpt B

"Societe Generale SA, France's second-largest bank by market value, said last week that unauthorized trades caused a $7.2 billion loss, the biggest in banking history. The trading wiped out about two years of pretax profit at the Paris-based company's investment-banking unit. Societe Generale said the trader [] had ``intimate and perverse'' knowledge of the bank's controls, which enabled him to avoid detection"

Excerpt C

"All of the risk-measurement tools failed to prepare Merrill for the unforeseen declines on triple-A rated securities backed by subprime mortgages, according to the company's third-quarter filing with the U.S. Securities and Exchange Commission. The firm's write-downs related to the highest-rated portions of CDOs backed by pools of home loans, which plunged in value as defaults on the underlying mortgages soared."

14.1 In the context of the above excerpts, comment on the shortcomings of VaR as a measure of risk, particularly during volatile market periods.           [5]

14.2 Identify and discuss the elements of financial risk raised in the three excerpts. [6]

Solutions:

Question 1

1.1 Old price = = R867.59

New price = = R933.41

HPR =   (7.58% without coupon)

OR most common method students used:

HPR =

= 11.29%

1.2 Imputed interest income

Calculate current price at original YTM

Price 872.66

P₀                     867.59

Interest                       5.07 (+60 coupon = R65.07)

Capital Gain/Loss

P₁                     933.41

P₀                     872.66

60.75

Total Change in Price = 65.82

After-tax return:

Tax on Interest                       = 1.521 (+(60 x 0.3) with coupon)

Tax on Capital Gain = 9.1125

After-tax return = 11.29% with coupon (6.36% without coupon)

1.3 Put Option (option to sell)

The holder would want to avoid the potential eroding effect of high interest rates on the current value of the bond. Therefore, upon agreement with the issuer he/she would be able to exit the agreement at par value. This option would serve to reduce the downside of the bondholder, however be less favourable to the issuer as he/she will have to forgoe a favourable lending arrangement

1.4 Call Option

The issuer would seek to avoid falls in interest rates resulting in him having to compensate the holder over and above that which is acceptable in the market. Allows the issuer to terminate the agreement and buy back the bond at a pre-specified price above.

As per the slides:

Callable Bonds:  Bonds that have a built in option for the issuer to repurchase the bonds at a pre-specified call price before maturity - allows issuer to save on interest payments by reissuing at a lower coupon

1.5 BESA: Bond Exchnage of South Africa

As per the slides:

.BESA offers listed bonds, listed interest-rate derivatives and unlisted derivatives.

.An integral element of BESA's core competencies is the maintenance and implementation of investor safeguards and international standards.

Primary user include: Dealer banks, securities lending houses, matched principal traders, brokers, bond issuers, asset managers and the SARB.

1.6 R153, R157, etc

Question 2

2.1 Size of Coupon

Larger coupon bonds are of lower duration due to their derived value being less sensitive to changes in the nominal value and associated interest rate volatility

Bond A lower coupon than Bond B, therefore bond B lower duration

Yield to Maturity

The higher the yield to maturity of the bond issue the less sensitive the bond price to changes thereupon

Bond A lower YTM than Bond B, therefore bond B lower duration

Note: Question 2.3 had two errors in the paper - firstly, it should have a stated period that is quarterly, and secondly it should reference Bond B, not Bond A. Credit was given regardless of whether students worked with A or B.

Question 3

3.1 f₁₂ = ((1.095)²)/(1.09) = 10.002%

f₂₃ = ((1.105)³/(1.095)²) = 12.53%

f₃₄ = ((1.12)⁴/(1.105)³) = 16.62%

3.2 The forward rates are used when analysing and evaluating the term structure of interest rates. Forward rates are calculated and compared with the market consensus expectations of future short rates.

Depending on the different theories of term structure (e.g. Expectations, Market Segmentation, Liquidity, etc.) these comparisons are then used for analysis and making investment decisions.

3.3 FALSE

Expected Short rates are notional and are simply expectations as to the behaviour of interest rates in future periods. Forward rates are computed from spot rates - being the yield on zero-coupon bonds of differing maturities.

3.4 TRUE

Both theories state that investors with differing time horizons can be swayed into to changing the term of their investment through the receipt of a substantial premium.

3.5 FALSE

Liquidity preference theory states that investors are averse to investing over a horizon they are not comfortable - perceive unfamiliar time horizons of higher risk.

Question 4

A rate anticipation swap is an active bond portfolio management strategy, based on predicting future interest rates. If a portfolio manager believes that interest rates will decline, the manager will swap into bonds of greater duration. Conversely, if the portfolio manager believes that interest rates will increase, the portfolio manager will swap into bonds of shorter duration. This strategy is an active one, resulting in high transaction costs, and the success of this strategy is predicated on the bond portfolio manager's ability to predict correctly interest changes consistently over time (a difficult task, indeed).

Question 5

C₀ + X e^-rt = S₀ + P₀

C₀ + 60 / e^{0.09 * 1} = 50 + 12

C₀ = 7.16

LA (+1 ; +1)

50 60

-50

7.16

SC60 ( 0 ; -1)

Overall:

SP60 (+1 ; 0 )

-42.84

(1 + R_PP)² + (1 + 0.09)

R_pp       = 4.4%

p = (1.044 - 0.9) / (1.05 - 0.9) = 96%

q = 1 - 96% = 4%

S₂₁ = 55.125

C₂₁ = 5.125

S₁₁ = 52.5 P₂₂ = 0

C₁₁ = 4.71

S₀ = 50   P₁₁ = 0.11 S₂₂ = 47.25

C₀ = 4.33                                               C₂₂ = 0

P₀ = 0.21 S₁₂ = 45 P₂₂ = 2.75

C₁₂ = 0

P₁₂ = 2.89 S₂₃ = 40.5

C₂₃ = 0

P₂₃ = 9.5

LC50 ( 0 ; +1)

50 54.33

-4.33

49.79

LP50 (-1 ; 0 )

49.79 50

-0.21

45.46 LSD50 (-1 ; +1)

45.46 50 54.54

-4.54

Question 6

a) MV = 665 000

(b)       w (EDCON) = (5000 x 45) / 665 000 = 34%

w (TELKOM) = (8000 x 55) / 665 000 = 66%

p = (0.34 x 0.70) + (0.66 x 1.10) = 0.964

(c) HR = (665 000 x 0.964) / (21000 x 10) = SF 3 contracts

[Total Marks = 45]

QUESTION 7 (7 MARKS)

(a)   Any one of these two advantages: (1) since the supply of gold is restricted, countries cannot have high inflation; (2) any BOP disequilibrium can be corrected automatically through cross-border flows of gold.

Anyone of these two disadvantages: (1) the world economy can be subject to deflationary pressure due to restricted supply of gold; (2) the gold standard itself has no mechanism to enforce the rules of the game, and, as a result, countries may pursue economic policies (like de-monetization of gold) that are incompatible with the gold standard.                                                                         [2]

(b)     An investor in emerging market stocks needs to be concerned with the depth of the market and the market's liquidity. Depth of the market refers to the opportunities to invest in the country. One measure of the depth of the market is the concentration ratio of a country's stock market. The higher the concentration ratio, the less deep is the market, i.e. most value is concentrated in only a few companies. In terms of liquidity, an investor would be wise to examine the market turnover ratio of the country's stock market. High market turnover suggests that the market is liquid, or that there are opportunities for purchasing or selling the stock quickly at close to the current market price.

(c)    A foreign bond issue is one offered by a foreign borrower to investors in a national capital market and denominated in that nation's currency. A Eurobond issue is one denominated in a particular currency, but sold to investors in national capital markets other than the country which issues the denominating currency. Moody's Investors Service and Standard & Poor's provide credit ratings on most international bond issues.  It has been noted that a disproportionate share of International bonds have high credit ratings. The evidence suggests that a logical reason for this is that the Eurobond/Foreign bond market is only accessible to firms that have good credit ratings to begin with. [3]

QUESTION 8 (6 MARKS)

(d)    ZAR spot rate under PPP = [1.08/1.13] (0.0741) = £0.0708/ZAR. [2]

(e)    Expected ZAR spot rate = [1.08/1.14] (0.0625) = £0.0592/ZAR.                        [2]

(f)      Expected ZAR under PPP = [(1.04)³/ (1.10)³] (0.0625) = £0.0528/ZAR. [2]

QUESTION 9 (6 MARKS)

QUESTION 10 (8 MARKS)

(a)    In the case of forward hedge, the rand cost will be 100,000,000/13.75 = ZAR7,272,727.27. In the case of money market hedge, the future dollar cost will be: 100,000,000(1.08)/(1.05)(15.5) = ZAR6,635,944.70.         [2]

(b)    The option premium is: (0.018/100)(100,000,000) = ZAR18,000. Its future value will be ZAR18,000(1.08) = ZAR19,440.

At the expected future spot rate of ZAR0.0727/„ (=1/13.75), which is higher than the exercise price of ZAR0.0648/„, PCC will exercise its call option and buy „100,000,000 for ZAR6,480,000 (=100,000,000x.00648).

The total expected cost will thus be ZAR6,499,440.00, which is the sum of ZAR19,440 and ZAR6,480,000.                                                            [2]

(c)     When the option hedge is used, HSA will spend "at most" ZAR6,499,440. On the other hand, when the forward hedging is used, HSA will have to spend ZAR7,272,727.27 regardless of the future spot rate. This means that the options hedge dominates the forward hedge. At no future spot rate, HSA will be indifferent between forward and options hedges.

(d)    Cross-hedging involves hedging a position in one asset by taking a position in another asset. The effectiveness of cross-hedging would depend on the strength and stability of the relationship between the two assets.                [2]

QUESTION 11 (12 MARKS)

(a)   Cross-country correlations tend to increase during the turbulent market phase, reducing the benefits from international diversification in the short run.                 [2]

(b)   The gain to be achieved through international portfolio diversification rests on the premise that security returns are much less correlated across various countries than within a country. Therefore, if during period of crisis, cross-country correlations are higher, the benefit achievable through international diversification is likely going to be eroded. An example is the current financial meltdown that we are experiencing, where we see security markets moving very closely across different countries. [2]

(c)    Factors that cause economies to behave independently and influence the correlations among international equity markets in the long run are:

i. the extent to which Government regulations is similar across countries

ii. the level of technological specializations of the countries

iii. similar or differing fiscal and monetary policies, and

iv. cultural and sociological differences.

(d)   Higher expected returns are anticipated from the emerging markets due to their higher expected economic growth. Analysts expect higher economic growth in emerging markets due to expected higher demand for their products both on the international and local markets. Low labour costs and low levels of unionization normally prevailing in these markets make their products very competitive on the export markets. Also, higher demand is expected from their domestic markets as standard of living of the local population improves.

Emerging markets offer opportunities for higher returns, but with a higher level of variation in those returns. Although the stand-alone risk of emerging markets is higher, much of the risk is diversified away in a global portfolio due to the low correlations with the developed world markets. The likely impact of including equities from emerging markets in a portfolio solely invested in developed market equities will result in a portfolio with higher return for the same level of risk, or lower returns for a given return.

(e)   In emerging markets, currencies are more volatile than in developed markets. Currency devaluations are common and central banks are usually weak. Currency devaluation would weaken the return of the foreign investor in his home currency. Stock returns and currency returns are usually positively correlated in emerging markets. In other words, in times of crisis currencies are frequently devalued and local stocks fall in value as foreign investors lose faith in the emerging economy. As such, in the case of downturn foreign investor usually suffers twice, with decreasing asset returns and decreasing foreign exchange value. Therefore, the trustees should be concerned and manage the currency exposure of their emerging markets investments.

QUESTION 12 (6 MARKS)

(a)  

Domestic Currency Return:

Portfolio : U.S. = [(1.11)*(1.1) - 1] = 22.10% and AUS = [(1.18)*(0.95) - 1] = 12.10%

Benchmark : U.S. = [(1.20)*(1.1) - 1] = 32.00% and AUS = [(1.14)*(0.95) - 1] = 8.30%

Excess Return in base currency = [(0.7*22.10%) + (0.3*12.10%)] - [(0.5*32%) + (0.5*8.30%)]

= [19.10% - 20.15%]

= -1.05%

(b) The currency allocation effect is 2.85%.

For U.S., (W_j,pC_j,p - W_j,bC_j,b) = 0.7(11.10%) - 0.5(12.00%) = 1.77%

For U.K., (W_j,pC_j,p - W_j,bC_j,b) = 0.3(-5.90%) - 0.5(-5.70%) = 1.08%

The market allocation effect is 1.20%.

For U.S., (W_j,p - W_j,b) R_j,b,f = (0.7 - 0.5) (20.00%) = 4%

For U.K., (W_j,p - W_j,b) R_j,b,f = (0.3 - 0.5) (14.00%) = -2.8%

The security selection effect is -5.10%.

For U.S., W_j,p (R_j,p,f - R_j,b,f) = 0.7(11.00% - 20.00%) = -6.30%

For U.K., W_j,p (R_j,p,f - R_j,b,f) = 0.3(18.00% - 14.00%) = 1.20% [1]

Question 13

13.1 First, we determine our exposures. We have an investment of NZ$255,000 in the NZX 50 index which is the equivalent of 255 000 x 5.65 = R1 440 750.  [1]

The dividend on the index, assuming the rate given is annual, is:

% x R1 440 750 = R2 161.13 [1]

12

The put options can be mapped back to the NZX50 index as follows:

= -0.56 x 2566.6 x 10 x 50 = -NZ$718 648. [2]

= 718 648 x 5.65 = R4 060 361

Given that both investments are in the same underlying asset we can net the position off to:

R1 440 750 - R4 060 361 = -R2 619 611 [1]

The currency exposure is simply the NZ$ value we have invested in the options plus the index. In this case we have (50 x NZ$4 375) + (NZ$255 000) = 473 750                  [1]

Next, we need to convert our variables to monthly data to match our VaR period.

For the currency risk exposure, we convert from annual to monthly:

[½]

[½]

For the NZX exposure, we convert from weekly to annual:

µ₂ = 0.54% x 4 = 2.16%                       [½]

σ₂ = 2.35% x 2 = 4.70%                       [½]

Lastly, we calculate our portfolio VaR.

_V = (-R2 619 611 x 0.0216) + (473 750 x 0.0113) + 2 161.13 = R49 069.1 [1]

_V (-R2 619 611 x 0.0470)² + (473 750 x 0.0677)² +

(2 x -R2 619 611 x 473 750 x 0.047 x 0.0677 x 0.23) = 14371149662

_V = R119 879.73                                 [2]

Therefore the 1-month 99% VaR is:

-R49 069.1 - 2.326 x R119 879.73 = -R327 909                     [1]

Your total investment value is given by the investment in the index and the investment in the puts:

(255 000 x 5.65) + (50 x 4375 x 5.65) = R2 676 688

Thus, your VaR represents R327 909/R2 676 688 = 12.25% of your total investment. [1] This is not within the 10% requirement you've set so the investment would not meet your requirements. [1]

(Alternatively, students could have calculated the relative VaR directly by dividing all exposure values in the mean and standard deviation formulae above by the portfolio value of R2 676 688).

14.1 The primary shortcoming of Value at Risk is that it requires the estimation of a distribution of underlying asset returns. This is typically derived from historical data which implies that most VaR calculations assume that prior market volatility will persist in future. The result is that significant market changes, such as the current sub-prime mortgage crises, are not factored at all into the VaR calculations as has been the case in excerpt A. The model is also only as good as its inputs which means that factoring in issues like credit risk would rely on the quality of the estimates used. In the case of excerpt C, there was a significant underestimate of credit risk for certain securities which meant that the VaR for these assets was also underestimated. The last issue relates to the fact that even at high confidence levels, VaR still has a margin of error, even when distributions are calculated as accurately as possible (e.g. at a 95% confidence level which most banks apply, there is still a 5% margin of error in the estimate).

14.2 The three aspects of Financial Risk that are raised in the excerpts above are market risk, operational risk and credit risk, respectively:

Excerpt A - Market Risk: risk that value of investment will decrease due to changes in market factors: e.g. changes in asset prices, interest rates (yield curves, credit spreads), currencies, inflation and commodity prices (metals, oil, etc). This is the typical risk factor that we use VaR to mitigate.

Excerpt B - Operational Risk: Risks arising from current or future losses due to failed or inadequate people, processes or systems, or external events. This is evident in the ability of the Society Generale trader to operate outside of the bank's monitoring systems.

Excerpt C - Credit Risk: Risk arising from failure of counterparty to meet its obligation as evidenced by the huge write-offs of sub-prime debt during the credit crisis.

Note: Students must have linked these risks back to the excerpts to earn full marks. Also, liquidity risk was accepted as a valid answer if it was linked back to the question.