ciia-Sample-Exam-PM-Questions

Sample Examination PaperFinal ExaminationSolutionsPortfolio ManagementDerivative Valuation and AnalysisFixed Income Valuation and AnalysisExam GuideQuestion 1: Bond Valuation and Analysis(a)Price of bond A = 8/1.0765 + 108/(1+1.0785)2 =100.28Price of bond B = 9/1.0765 + 9/(1.0785)2+ 109/(1+1.0805)3 = 102.51(b)Duration of bond B:Cash flowPV (using YTM of 8.027%)t × PV 98.338.3397.7115.4210986.46259.38Total 102.5283.13Duration = 283.13/102.5 = 2.76 yearsChange in price due to change in yield:dP = – D × P × dR/(1+R) = – 2.76 × 102.51 × 0.002/1.08027 = –0.52The change in price is +/– 0.52 per 100 nominal.(c)In 1 year’s time:P A *= 1081075.=100.51P P A A *−=100.51 – 100.28=0.23C P P P A A A A +−()×=+×=*...%1008023200281008207(Note: they receive coupon + price change over 1 year for holding period return)In 1 year’s time:P B *= 91075109107652..+()=102.43C P P P B B B B +−×=+−()×=*....%1009102431025110251100871(d)If your view is different to that of the market — as outlined in assumption (i) (e.g.you believe that a rising yield curve will remain the same) then you will not achieve the expected holding period returns calculated as in (c). If, on the other hand, you believe the assumption in (ii), then you expect the holding period returns estimated in (c) to be achieved.Exam GuideQuestion 2: Bond Valuation and Analysis(a)(i)From the following formula:∆∆∆∆∆∆P PD r P P D r r r =−×⇔=×−×()×−()×()−×−()×()−<120611012100we can see: ∆r < ∆0.0167(where ∆r = interest-rate change and D = modified duration of bonds (years))In other words, the surplus will be negative if interest rates fall 1.67 percentage points or more.(ii)From the following equation:804041101212024200410×−()×()+×−()×()−×−×()[]+−D r r r ∆∆∆..we can see: D = 14.5(where D = modified duration of bonds)In other words, the modified duration of the bonds should be 14.5 years.(iii)From the following equation:(120 × –D × ∆r) – (110 × –12) × ∆r) = 0we can see: D = 11.0In other words, the modified duration of the bonds should be 11 years.(iv)Even if the bond weighting is small, the duration of the bonds can belengthened so that the duration of pension assets as a whole matches theduration of pension liabilities, which reduces interest-rate risk. In doing this,the equity component can be increased to cover the reduction in bonds, which will increase the expected long-term return on the asset side. However, this also increases risk from stock price movements, a different risk than the interest-rate risk considered here.(b)(i)Inflation will result in an increase in nominal interest rates and therefore lowerthe market price of bonds (assets). Pension liabilities are virtually unchangedbecause the increase in future benefit amounts is offset by the increase in thediscount rate (nominal interest rate).(ii)When pension benefit amounts are indexed to inflation, it is essentially thesame as benefit amounts being fixed in real terms, so the liability (presentvalue) is found by discounting the benefit amount using real interest rates.(iii)Pension liabilities essentially move dependent on real interest rates, so that aninvestment in “CPI-linked bonds” for which prices change according to realyields will result in a matching of bond and liability durations in terms of real interest rates. If these bonds are not available, bearing in mind that short-term instruments provide a good hedge against inflation, short-term bonds orvariable rate interest-bearing bonds should be used.Exam GuideQuestion 3: Derivative Valuation and Analysis(a)(V – 16)/16 = 0.03 + 1.2 × [(T – 1,600)/1,600 – 0.03]Rearranging this: V = 0.012T – 3.296 (¥ billion)(b)(i)Assuming X is the strike price, Y the number of contracts, payoff at expirationis:V + 0.00001Y max [X – T,0]= 0.012T – 3.296 if T > Xor (0.012 – 0.00001Y)T + 0.00001XY – 3.296 if T < XTherefore, from 0.12 – 0.0001Y = 0Y = 1,200 contractsFrom 0.00001XY – 3.296 = 16X = 1,608(ii)Cost of hedge = put price × no. of contracts × TPOIX option: index76.3 × 1,200 × 10,000= ¥915,600,000(c)(i)Relationship between change of TOPIX and the price of puts:∆P = –0.406 ×∆TRelationship between change in TOPIX and futures price:∆F = (1 + 0.03/12) ∆TTherefore, you need to sell1,200 × [0.406/(1 + 0.03/12)] = 486 contracts(ii)You now need to sell1,200 × [0.355/(1 + 0.03/12)] = 425 contractsSo you need to buy back–425 – (–486) = 61 contracts(iii)When volatility is high, the number of contracts you need to sell for hedging becomes larger. In this case, you will suffer a loss because the number of futuresyou have sold is smaller than is necessary.Exam GuideQuestion 4: Derivative Valuation(a)(i)Sell calls only.(ii)The return from the strategy will be generated from:•the change in BHP share price;•income from call selling; and•dividends received.There is a risk of loss if the income generated from call writing and dividendsdoes not compensate for any fall in the BHP share price.(iii)Sell stock, sell puts.(b)(i)Buy straddle/strangle (or short condor or short butterfly are acceptable.)—5—10—15—20—25June SPI futures(ii)•option delta•beta of portfolio.(c)(i)Long 2000 shares.(ii)It would increase due to the high gamma of the April calls.(iii)Sell April calls due to high theta — they will expire worthless in two weeks if stock stays at 9.50. Sell more June 9.00 puts or buy stock back to increaseexposure back towards neutral.(d)(i)Implied higher, due to wide expectation of price movement.(ii)Implied lower, due to low expectation of price movements from takeover level.Note: The markets and shares referred to in these questions may beinterchanged with other markets and shares for other countries, as the sameprinciples should apply.Exam GuideQuestion 5: Portfolio Management(a)This is an example of static portfolio insurance. The portfolio value at maturity is atleast 100% of the invested capital or more, depending on the Index level at maturity.If the Index level at maturity is higher than the Index level at starting date, you get a fraction (or even a multiple) of the Index performance (performance ×P).The described protection profile can be obtained with S&P500 calls. First of all, the present value of the guaranteed floor (invested capital discounted according to theduration) has to be invested in risk-free zero-coupon bonds with a correspondingmaturity. The proceeds are invested in at-the-money spot (strike = Index level atstarting date) S&P500 European style calls with the same maturity. Then the bankcan leave the position until maturity.(b)The parameter P is the participation rate (e.g. it determines by how much you canparticipate in a positive S&P500 index performance). P is determined by two market parameters. The first one is the risk-free interest rate (according to the duration),which determines the price of the bond and therefore the remaining amount that can be invested in calls (e.g. higher interest rate => lower bond price => more calls =>higher P). Furthermore, the interest rate influences the price of the calls (higherinterest rates => higher call price => lower P). The interest rate effect on the price of the bond usually dominates the effect on the call price (overall, higher interest rates => higher P). The second market parameter is the volatility of the S&P500 Index (or rather the implied volatility which has to be paid), which influences the price of the calls (higher volatility => higher call price => lower P). Another factor that has animpact on P is the chosen maturity of the product. On the one hand, a longerduration means a longer time to discount the guaranteed floor (e.g. if the yield curve is not too inverse, you have a lower bond price which results in a higher amount to invest in calls => higher P). On the other hand, a longer duration means a higher call price (ceteris paribus) => lower P. Thus, whether P is higher or lower depends mainly on the interest rates and volatilities.Exam Guide(c)Here you have a cap level (e.g. the payoff has a maximum value). If the index level atmaturity exceeds Imax, the payoff is constant.In addition to the actions in (a) above, the bank would sell S&P500 calls (samenumber as long calls) with a strike price which is higher than the Index level atstarting date. In other words, the proceeds (after buying the zero-coupon bond) areinvested in bull call spreads (lower strike price = Index level at starting date) insteadof only long calls.(d)In the second version with the cap level you receive money for the short calls (e.g. onecall spread is cheaper than one long call), so you can buy more call spreads (secondversion) than long calls (first version). Thus the participation rate P is higher in thesecond version until the index level at maturity does not exceed a certain value Ibe , asyou can see in the following graph.Exam Guide(e)Yes, it has an impact. If a lower Imax is chosen, the call spread is cheaper (you receivemore money for the short call), so you can buy more call spreads. Therefore theparticipation rate is higher (but the cap level is lower). Correspondingly, you have a lower P with a higher cap level if a higher Imaxis chosen.Question 6: Portfolio Management(a)The more efficient the market is, the lower the IR (which is an expression of theactive manager’s skills) will be. Theory would therefore dictate that allocation toindividual active managers be decreased, and, as a result, allocation to passivemanagers would increase.(b)Allocations to individual managers would be as follows:A: (20/2) × (0.20/10.0) = 0.20B: (20/2) × (0.20/8.0) = 0.25C: (20/2) × (0.10/5.0) = 0.20P: 1 – (0.20 + 0.25 + 0.20) = 0.35(c)When there is a positive correlation between excess returns, the combined trackingerror of the two will be larger than when they are mutually independent and as aresult, the IR will be smaller. This would dictate a reduction in allocations to A andB. The allocation to C would not change because it is independent of A and B. Thereduction in allocations to A and B would therefore result in an increase in theallocation to P.(d)Generally speaking, the larger the amounts involved, the lower the returns fromactive investments, for several reasons: there are limits to the number of stocksproviding α, high-volume trading will have a “market impact”; and costs willotherwise rise as well. Therefore, if one increases allocations (amounts undermanagement) according to past IRs, there is a chance that the α will be lower than in the past.Question 7: Portfolio ManagementThe main problem as soon as the portfolio has been constructed is the potential monthly rebalancing needed in order to realign your portfolio with the benchmark. In fact if the 50%/50% weighting is valid at the beginning of a month, there is very little chance that this weighting scheme will still be same after one month (unless performances of SMI and MSCI Europe are exactly the same). The index will automatically and without any cost be realigned towards the initial weights, while the portfolio will have to bear the transaction costs for such regular rebalancing.There will be a negative drag on the relative performance due to transaction costs. Furthermore, there is a danger of a high turnover when adjusting on a monthly basis if markets tend to exhibit trend reversal performance in the long run.On the positive side, a regular turnover can help the manager to adapt smoothly to the continually changing structure of the benchmark.Exam GuideQuestion 8: Portfolio Management(a)SV: 2 + (0.85 × 8) + (0.8 × –2) + (1 × 0.1) = 7.3%SG: 2 + (0.95 × 8) + (1.3 × –2) + (1 × 0.1) = 7.1%LV: 2 + (0.90 × 8) + (2 × –2) + (8 × 0.1) = 6.0%LG: 2 + (1.10 × 8) + (3 × –2) + (10 × 0.1) = 5.8%We choose the portfolio Small Value.(b)either: 2 + (1 × 8) + (2.405 × –2) + (8.3 × 0.1) = 6.02% or:7.3 × 5/100 + 7.1 × 5/100 + 6 × 40/100 + 5.8 × 50/100 = 6.02%The market is a weighted average, thus its return is bounded by the 4 portfolios.(c)SV: 2 + (0.85 × (10 – 2) = 8.8%SG: 2 + (0.95 × 8) = 9.6%LV: 2 + (0.90 × 8) = 9.2%LG: 2 + (1.10 × 8) = 10.8%The competitor chooses the portfolio Large Growth.(d)where x = market betax1 + x 2 = 1(x1 × 0.85) + (x2 × 1.1) = 1so if x2 = 1 – x1 then,(x1 × 0.85) + ((1 – x1) × 1.1) = 1thus x1 = 0.40 and x2 = 0.60.The other competitor puts 40% of her portfolio in Small Value and 60% in LargeGrowth.。