Profit from FX Volatility

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Derivatives & Currency Management

Swaps, Forwards & Futures Strategies

Motivation: Profit from FX Volatility 3 Volatility Strategies è 1.Long Straddle = LC ATM 50D + LP ATM 50D, debit strategy (investment), bet big currency moves in either direction (∨ shape), expensive strategy, D neutral 2.Short Straddle = SC ATM + SP ATM, credit strategy receive 2 premiums, bet on flat market – stable spot (∧shape) income 3.Long Strangle = LC OTM 25D + LP OTM 25D, cheaper strategy (bowl shape)

Put Deltas – negative values Call Deltas – positive values | | | | | | | | 50 25 10 10 25 50 100 delta 100 delta Quoted in Deep ITM delta delta Delta Absolute delta delta delta Deep ITM terms Very ATM OTM OTM OTM OTM ATM Very Expensive Expensive cheap cheaper cheaper cheap Expensive Expensive Premium Premium Cheaper 0 = OTM Cheaper BBox 3 Q4 BBox 6 Q2 & 3 But more downside risk Cheapest BBox 5 Q4 Premium R15 Options Sec. 4.1.3.2 BBox 8 Q2

3 Volatility Trades using Currency Options 1. Profit in High Volatility Mkts 2. Profit in Low Volatility Mkts Motive: FX appreciates or depreciates Motive: FX stays flat, collect 2 premiums Long Straddle = LC ATM + LP ATM Short Straddle = SC ATM + SP ATM Exercise Price LP ATM 50D LC ATM 50D Profit Profit ------

+ + - + - - FX Price FX Price Loss ------Loss Exercise SP ATM 50D SC ATM 50D Price Expensive! Asset better NOT move!!

• Time value (theta) 3. Cheaper Bet on Large Moves • Short Strangle declines as they • Long Strangle = LC OTM + LP OTM SC OTM + SP OTM move toward expiration LP OTM LC OTM 25, 10 or 0D Less income in Profit 25, 10 or 0D flat markets, safer • Options have no + + strategy opportunity costs - FX Price ------Less expensive! but require cash Loss ------for upfront Exercise Price premium pmts BBox 3 Q4 R15 Options Sec. 4.2 3/1/21 BBox 8 Q4 LevelUp, LLC©2021 All rights reserved 5

Ways to Reduce Hedging Costs - part I It is expensive to remove all currency downside risk. Hedging is insurance against adverse currency movements but portfolio managers can overpay for protection

Protective Puts using OTM (not ATM) Options “Increase deductable to reduce premiums” • Protective puts using ATM 50D options is very expensive, buys convexity • Alternatively, use cheaper OTM 25D or deeper OTM 10D options that are less costly but come with more downside risk & less protection

Reduce protective put hedge costs by selling or “writing” options

Short Risk Reversal (Collar) Long Risk Reversal = LP OTM + SC OTM + Long FX = LC OTM + SP OTM + Short FX • “Zero-cost collar” strategy where a • Another “collar” strategy where the long 25D put is expensive but cost long 25D call is expensive but cost BBox 6 Q1 reduction comes from selling 25D reduction comes from selling 25D call = “short 25D risk reversal” w/ put = “long 25D risk reversal” w/ BBox 8 Q3 long base, bearish & uncertain vol short base, bullish & uncertain vol Exhibit 9 EOC 21 Reverses volatility skew! R15 Options Sec. 3.5 3/1/21 LevelUp, LLC©2021 All rights reserved 6

Ways to Reduce Hedging Costs - part II

“Bear” Put Spread = LP OTM 25Δ + SP deeper OTM 10Δ • Used only when modest depreciation in the exchange rate is expected • Limited downside protection – unhedged below deeper OTM 10Δ short put @ 1.345 • Position must be closely monitored • Not a zero-cost position 25Δ put ≠ 10Δ put • Alternative methods to reduce costs: • Use closer strike prices - 1.3525 • Use larger notional amount on the deeper 10ΔOTM SP “1 x 2 put spread” X X X SP 10-delta LP 25-delta Spot FX 1.3450 1.3500 1.3550 Unhedged Hedged Unhedged

R15 Options Sec. 4.1.2

Ways to Reduce Hedging Costs - part III “Winged” creature option strategies (Seagulls & Butterflies – R33) involve 3 or 4 options. The “wings” are options with most distant OTM strikes & the body is the middle ATM strike. In all cases, manager is long the base currency in the P/B quote

Short (wings) Seagull Spread Long (wings) Seagull Spread SP OTM + LP ATM + Long FX + SC OTM LP OTM + Long FX + SC ATM + LC OTM

Bear Put Spread + Covered Call Long Strangle + Covered Call • Spot FX at 1.355 • Spot FX at 1.355 • Protective put w/ long ATM put @1.355 • Long strangle with OTM LP + OTM LC • Short OTM put & call ê hedge cost • Short ATM call ê hedge cost Short OTM Put @ 1.350 - wing Long OTM Put @ 1.350 - wing Long ATM Put @ 1.355 - body Short ATM Call @1.355 - body Short OTM Call @ 1.360 - wing Long OTM Call @ 1.360 - wing • Downside protected 1.355 to 1.350 • Cheap downside risk protection - OTM LP • Limited upside 1.35 to 1.360 SC strike • Unlimited upside if FX appreciates above • Collect two premiums on SP & SC 1.360 long call strike • Safe strategy since long put is ATM • Buying two options LP & LC - more costly BBox 6 Q1 3/1/21 LevelUp, LLC©2021 All rights reserved 8

BIG PICTURE Option Strategies Currency Options Fixed Income

Covered Call = U/L + OTM SC Income Bond “duration neutral” portfolio structure Protective Put = U/L + ATM LP Hedge Protective Put = Long FX + ATM LP strategies NOT option strategies Long Straddle = ATM LP + ATM LC Long Straddle = ATM LP + ATM LC

Volatility, directionless trades Long Strangle = OTM LP + OTM LC 3 Bond Short Straddle = ATM SP + ATM SC Short Straddle = ATM SP + ATM SC Strategies

Short Straddle = OTM SP + OTM SC

Collar = Long U/L + LP + SC Hedge Short Risk Reversal Long Butterfly = Long 2s = Long FX + OTM LP + OTM SC + Short 7s + Long 30s Short Butterfly = Short 2s Long Risk Reversal + Long 7s + Short 30s = Short FX + OTM SP + OTM LC

Bear Put = ITM LP + OTM SP Bear Put = OTM LP + OTM SP 4 Bonds Bull Call = ITM LC + OTM SC 1 x 2 Bear Put = ITM LP + 2 OTM SP

Bull Put = ITM SP + OTM LP Small Hedge U/L Short Seagull = OTM SP + Bear Call = ITM SC + OTM LC moves ATM LP + Long FX + OTM SC Long Condor = Long 2s + Long Calendar = Sell near + Buy Far Short 5/10s + Long 30s Long Seagull = OTM LP + Theta decay trade Short Condor = Short 2s + Long FX + ATM SC + OTM LC Short Calendar = Buy near + Sell Far Long 5/10s + Short 30s 3/1/21 LevelUp, LLC©2021 All rights reserved 9

Fixed Income Portfolio Management

Introduction to Fixed-Income Portfolio Management Liability-Driven & Index-Based Strategies Yield Curve Strategies Credit Strategies

Fixed Income Portfolio Management (1)

Introduction to Fixed-Income Portfolio Management Liability-Driven & Index-Based Strategies

Decomposing Bond Returns - 5 Parts 1 2 3 4 5 Yield income or Rolldown return Expected D in Expected Currency - + E(r) = Income yield* + “Aging” + yields & yield credit loss gain/(loss) Prob default x * Includes interest on “Riding the YC*” spreads ( Loss severity) reinvestment income Pull to par effect & earns YTM R20 R21 Sec 6 R17 Exp. Annual coupon (Price – Price ) = 1 0 [– MD x ∆ Yield] + [½ x Convexity x (∆ Yield)2] Return + + Current bond price Price0 If portfolio holds embedded option bonds, use effective Rolling yield EOC 2 duration & convexity No change in yields Exh 8 • Notional principal = €100mm Example • Annual coupon (per €100) = €1.5 • Income yield = 1.5/98.00 = 1.5306% annually • Current avg. price = €98.00 • Rolldown = (98.50 – 98.00)/98.00 = 0.510% • Exp. price in 1yr. = €98.50 • Rolling yield = 1.53% + 0.51% = 2.0408% • Avg. bond convexity = 18 • Exp. price change based on yields & yield spread • Avg. bond MDur = 4.0 = [–4.0 x 0.0025] + [1/2 x 18 x (0.0025)2] = –0.994% • Exp. avg. yield & spread ∆ = 0.25% • Credit loss = – 0.10%

• Exp. credit loss inv. grade = 0.10% • Currency depreciation = – 0.20% R20 Carry Trade • Exp. currency loss = 0.20% Total exp. return = 0.747% BBox 5 – Q1 R20 Riding YC* Sec 3.1.2 BBoxes 5* & 6 EOC 11 2018 Q7D 3/1/21 LevelUp, LLC©2021 All rights reserved 12

Leverage Increases Returns & Risk… Leverage magnifies investment returns by borrowing at low cost 4% & attempting to earn a greater rate of return 5% on invested funds. Leverage used within a fixed income portfolio is highly susceptible to interest rate sensitivity (magnifies duration – price risk)

Leverage Fundamentals • More leverage used, the higher sensitivity to IR changes • Higher variability of invested fund returns can lead to higher outcome uncertainty risk

Market Value of Bonds – Borrowed Funds = Equity Levered return = fund return + (borrowed funds/equity)(fund return – borrowing rate)

rp = rI +(B/E)(rI – rB)

MV Bonds Borrowed Funds Equity Levered Return - rp Assets = Liabilities + Equity rp = 5% + (100/30)(5% − 4%) rp= 8.3% $mm 130 100 30 rp= (32.5 − 30.0)/30.0 = 8.3% Earn rI /(cost rB) 5% 4% • Fund unlevered return = 5% Position 136.5 104.0 32.5 • If the fund return was 2% instead of 5%, the equity return = − 4.7% 2012 Q7 R25 Eq Port Const Sec 4.2 EOC 3

Fixed Income Portfolio Management (1)

Introduction to Fixed-Income Portfolio Management Liability-Driven & Index-Based Strategies

Immunization = Zero Replication Strategy • Interest rate hedging strategy that minimizes the variance of the realized return • “Zero replication” strategy “6 yr. zero” matches the single liability 6 yr. horizon date • NOT a passive approach - requires frequent rebalancing to match duration target • Immunization risk: YC shifts/twists thus CF yield bond portfolio ≠ zero coupon YTM EOC 2, 12- “Perfect These need to match for 15,19 & 24* match but not single liability immunization available” to work 2018 Q7A BBox 2* Zero Coupon Bond Coupon Bonds…James Bond! • Macaulay durations match = Set portfolio Macaulay duration = liability due date

• Face value (discount) = Initially MV bond portfolio exceed or match PVLiability • No dispersion or convexity = Minimize bond convexity & cash flow dispersion

Structural Risk Exh. 8 Some D Curvature – • D portfolio CF yield is not the Parallel shifts yields rise structural risk same as zero-coupon YTM • Caused by yield curve twists & Steepening Negative non-parallel shifts – D curvature Twist Immunization While some yields Reduce structural risk use zeros, lower works fall & YC flattens convexity & minimize CF dispersion 3/1/21 EOC 21 LevelUp, LLC©2021 All rights reserved Exh. 7 & 8 15

4 Multiple Liability Immunization Strategies 1. Cash Flow Matching 2. Duration Matching • Held-to-maturity, high quality • Match asset money (dollar) duration to gov. bonds or zeros used liability money (dollar) duration to match the amount & • Use investment grade bonds - cheaper timing of financial liabilities • $Duration = Modified duration x MV • Accounting defeasance – • Basis point value (BPV) = $Dur x 0.0001 where both asset & liabilities are removed from B/S • When MVAssets ≠ PVLiabilites, match BPVs

All these portfolios are Multiple Liability Immunization Conditions designed & structured to • MV > MV (3 bonds in exh.3) track the performance of a Assets Liabilites zero-coupon bond that • BPVAsset = BPVLiability locks in a rate of return to meet a liability • ConvexityAsset > Convexity_ Liability minimizes dispersion EOC 3 2017 Q9 3. Derivatives Overlay 4. Contingent Immunization • IR futures to close duration gap • Hybrid passive-active mgt of the surplus (synthetic) – cheap rebalancing tool account (any asset class) where the # contracts = (BPVLiability – BPVAsset) manager can pursue active mgt. as long BPVFutures as surplus is above a threshold value + Buying futures, increases duration • Goal: reduce cost of retiring the liabilities

Cash Flow Matching Example Liability Gov. Bond A par required = £5,250,000/1.055 Due Liability Bond Coupon (reduces par value needed by final 5.5% coupon) Dates Payments Maturity Rate = £4,976,303 round up to £4,980,000 par value June 2018 £3,710,000 L1 May 2018 2.75% maturing May 2021 Bond A coupon £273,900 = £4,980,000 x 5.5% June 2019 £6,620,000 L2 May 2021 3.50% Bond B par required = £4,410,000 – £273,900 June 2021 £4,410,000 L3 May 2021 4.75% = £ 4,136,100 Reduce £ 4,136,100 for final 4.75% coupon = June 2021 £5,250,000 L4 May 2021 5.50% £3,950,000 par value + £187,625 (= 4.75% x *£10,000 minimum denomination purchases £3,950,000) Bond D C B A Bond C par required = £6,620,000 - £273,900 - Liabilities L1 L2 L3 L4 £187,625 = £6,158,475 Reduce £6,158,475 for a final 3.50% coupon = £5,950,000 par value + £208,250 = 3.50% x Time 0 2018 2021 2021 2021 £5,950,000

Bond A retires L4 = ACoup + APrin L4 CF’s £5,253,900 = £273,900 Acoup + £4,980,000 Aprin (excess 3,900)

Bond B retires L3 = ACoup + Bcoup +BPrin L3 CF’s £4,411,525 = £273,900 + £187,625Bcoup+ £3,950,000Bprin

Bond C retires L2 = Acoup+ Bcoup+ CCoup + CPrin L2 CF’s £6,619,775 = £273,900 + £187,625 + £208,250 Ccoup + £5,950,000 Cprin Bond D retires L1 = Acoup+ Bcoup+ CCoup + Dcoup + DPrin BBoxes 3* & 4 3/1/21 LevelUp, LLC©2021 All rights reserved 17

Duration Matching

Multiple liability duration match strategy set BVPAsset = BPVLiability

Duration Matching Assumptions Liability Assumptions (Exh 4)

1.Expect future parallel shifts in YC • PVLiabilities = €200,052,250 (3 bonds) 2.Bond types & quality match liabilities • Cash flow yield = 3.7608% 3.Rebalance by buying & selling bonds L • Macaulay duration = 6.0004

EOC 5 Step 1: Calculate • Modified duration = Macaulay duration/(1 + CF yield per period) modified duration • Annualized modified duration = 6.0004/(1 + 0.037608/2) = 5.8896

Step 2: Calculate Yes, this is correct! • Money (dollar) duration = Modified duration x MVLiabilities money € duration • Money duration = 5.8896 x €200,052,250 = €1,178,237,935

• Basis point value (BPV) = Money duration x 0.0001 Step 3: Calculate • BPV = €1,178,237,935 x 0.0001 = €117,824 basis point value • For a 1 bp change in cash flow yield, liability changes by €117,824 BPV or PVBP • Money gained or lost for each one basis point change in yield 3/1/21 LevelUp, LLC©2021 All rights reserved 18

Duration Matching Example Assumptions Exh 4, 10 & 11

• MVAssets (Immunizing bonds) = €202,224,094 (Investment grade bonds)

• PVLiabilities = €200,052,250 1 Surplus = $2,171,844 • Bond cash flow yield = 3.5822% (IRR x 2) annualized cash flow yield • Macaulay duration = 11.8615/2 = 5.9308 (time weighted PVCFs) • Modified duration = 5.9308/(1+0.035822/2) = 5.8264 Annualized • Dispersion = 49.194/4 = 12.30 values • Convexity = 201.7767/[(1+0.035822/2)]2 = 194.73/4 = 48.68

Statistics Immunizing Bonds Corp Debt For a multiple liability

Value €202,224,094 > €200,052,250 immunization strategy with > equal asset & liability Cash flow yield 3.5822% 3.7608% durations, a more convex portfolio outperforms a less BPV 117,824 = 117,824 2 convex portfolio (higher gains if yields fall & lower Dispersion 12.30 > 8.26 losses if yields rise) EOC 5 & 26 Convexity 48.68 > 45.54 3 BBox 4* Portfolio B D MV of the bonds = D MV liabilities when yields rise/fall Exh 12 – Parallel shift (works) steep & flatten Will not qualify for accounting defeasement (structural risk occurs) 3/1/21 LevelUp, LLC©2021 All rights reserved 19

Derivatives Overlay Example Cost effective method to synthetically adjust asset duration to match liability duration

Corporate Debt Liabilities Duration Gap

• PVLiabilities = $200,052,250 GAP = BPVAssets − BPVLiab • Macaulay duration = 6.0004 • Yields rise by 100bps • CF Yield = 3.7608% • Yields & duration (prices) are inversely related, thus • BPVLiability = $117,824 • MVAssets & PVLiabilities fall

• BPVAsset = $18,819

Surplus = $22,697,750 • BPVLiability = $117,824 Using interest rate derivatives • Duration gap = − $99,005 Portfolio of Government Bonds

• MVAssets = $222,750,000 • High-quality, short-term bonds are more liquid & met regulatory requirements • Macaulay duration = 0.8532 • CF Yield = 1.9804% (high quality, short-term bond yields) rd • PVLiabilities @ 1.9804% = $222,552,788 (Exh. 4 – 3 column)

• BPVAsset = Macaulay duration/(1+ CF Yield/2) x MVAssets x 0.0001

• BPVAsset = 0.8532/(1 + 0.019804/2) x $222,750,000 x 0.0001 = $18,819

Exh 13 Solve for Nf & Cheapest Bond Qualifying CTD Bonds 6 ½ Yr. T-Note Ultra 10 Yr. T-Note Coupon rate 2.75% 4.00% Maturity Date November 15, 2023 February 15, 2027 Full price per 100,000 in USD 94,449 USD 99,900 par value Yield to maturity 3.8088% 4.0122% Modified duration 6.0215 8.1742

BPVCTD per 100,000 par 56.8727 81.6607 Conversion factor CTD 0.8226 0.8516

BPVFutures 56.8727/0.8226 = 69.137 81.6607/0.8516 = 95.8909 Futures Problems BPVFutures = BPVCTD/CFCTD Eq. 2, 3 & 4 • Daily monitoring N = (BPV – BPV )/BPV f Liability Asset Futures • Mark-to-market 6 1/2 Yr. T-Note 10 Yr. T-Note N = (117,824 – 18,819)/69.1377 N = (117,824 – 18,819)/95.8909 f BBox 5 f Buy 1,432 contracts 2018 Q7B Buy 1,032 contracts, closes duration gap!

Contingent Immunization Hybrid passive-active strategy whereby a manager, with a total return mandate, pursues active strategy if there is a significant surplus (MVAssets > MVLiabilities) above a designated threshold. If surplus shrinks, mandate reverts to a passive duration match

Example Gov Bonds Corp Debt • Surplus = £13,618,947 Market value £64,271,055 £50,652,108 • Negative duration gap = - £12,114 Modified duration 3.75 7.15 • Manager is currently long 160 futures contracts 10-yr. £100,000 BPV £24,102 £36,216 par gilts with BPV of 98.2533 • What best describes the Nf = (BPVLiability – BPVAsset)/BPVFutures Eq. 2 & 3 manager’s objective & what is her view on interest rates? Contingent Immunization

Nf =(36,216 – 24,102)/98.2533 = • Invest surplus in any asset class Nf = long 123 contracts • “Achieve gains & reduce cost of liabilities” • Manager is over- hedged with • Asset class liquidity is VERY important 160 long contracts vs. 123 in an attempt to gain when interest rates Fixed Income Overlay Strategy fall (gilt futures prices rise), further • Over-hedge: expect rates to fall, prices rise increase surplus & reduce cost of • Under-hedge: expect rates to rise, prices fall retiring debt liabilities R13 Prin AA Sec 3.2.2 BBox 6 3/1/21 LevelUp, LLC©2021 All rights reserved 22

Close the Gap Using Futures or Swap? • DB plan believes rates falling Pay 3-month LIBOR • 30yr. receive fixed, pay floating swap …or FRN Swap Dealer • Swap effective duration = +16.73

• BVPSwap= +0.1673 per $100 NP Receive 4.16% Fixed Exh 15 Asset Alloc % MDur +Swap Duration = DurationFixed rate bond – DurationFloating rate note Equity 50% 0 • Positive duration for the pension – receiving fixed Fix Inc. 40% 5.5 Alt Inv. 10% 0 • Negative duration for the swap dealer Mario - paying fixed

BPVAsset = Asset alloc. weight x modified duration x MVassets x 0.0001

BPVAsset = [(50% x 0)+(40% x 5.5)+(10% x 0)] x $2.7 billon x 0.0001 = $594,000

100% Hedging Ratio PBO BPVLiability = $2,257,080 CLOSE GAP Eq. 3 4 METHODS

1. Ultra 10yr Futures – Nf ? 2. Rec’v Fixed Swap Notional Principal BBox 7

Nf = (BPVLiability – BPVAsset) BPVAsset + [NP x BPVSwap/100] = BPVLiability Eq. 6

BPVFuturesUltra10yr NP = (BPVLiability – BPVAsset)/BPVSwap x 100

Close the Gap Using Swaption or Swaption Collar Hedging Ratio (HR) 3. Purchase Receiver 3.5% Swaption • HR = % of duration gap to close, • Buy an option to enter fixed-rate recv’r swap depends on interest rate view Exh 16 • 100% fully hedged = $994mm swap Gains NP or 17,343 futures contracts below 3.5% Yields need to • 50% hedge = $994mm/2 = $497mm fall by 66 bps • Strategic hedging - active mgt. of HR Loss 4. Swaption Collar above 5.0% if $4.97mm rates rise = Buy Receiver + Sell Payer premium • Long 3.5% receiver swaption + Short • Strike @ 3.50%, upfront cost known 5.0% payer swaption = Zero premium • Current 30yr. fixed rate swap @ 4.16% OTM • Below 3.5%, long swaption gain ITM, • Pay premium 1% x $497mm NP = $4.97mm option exercised, DB receives fixed • Yields below 3.5% - DB exercises swaption 3.5% & CP receives lower floating pays LIBOR & receives rates above 3.5% • Between 3.5%-5.0%, swaptions OTM DB is HERO if rates fall & • Above 5.0%, payer swaption ITM to 1. Receive fixed rate swap @ 4.16% counterparty & DB is obligated to receive 5% with rates going higher 2. Long receiver swaption @ 3.5% • DB may close out contract with CP 3. Enter swaption collar Wht Text Exampl e R16 Sec. 2 Swaps BBox 8 Q1 3/1/21 LevelUp, LLC©2021 All rights reserved 24

Fixed Income Portfolio Management (2)

Yield Curve Strategies

Oh Carry I’m in love! Intra Market Carry Trade Example Goal: Earn higher income, increase yield (no FX yet!) Curve Intra-Market - Single Currency Swap Rates - Various Maturities Shape • Exploit upward sloping YC – IR risk Floating rates Finance short end/receive higher rates 1. Borrow @ repo rate/buy long bond 2. Receive fixed – pay floating IR swap 3. Buy/long bond/note futures Quoted annual rates, semi-annual payments Exh 8

Intra-Market Trade Intra-Market Trade Intra-Market Trade GBP YC NZD YC MXN YC Buy 5yr & receive 0.84% Buy 5yr & receive 2.92% Buy 1yr receive 7.28% Finance 6 mo. rate (0.47%) Finance 6 mo. rate (2.03%) Finance 6 mo rate (7.19%) =0.37/2 = 18.5bps 6 mo carry =0.89/2 = 44.5bps 6 mo carry = 0.09/2 = 4.5bps 6mo carry

Inter-Market Carry Trade Example Sonia Alexis Goal: Exploit spread between YCs Inter-Market - Multiple Currencies & YCs Swap Rates - Various Maturities • Borrow @ low interest rate currency, lend (buy) in another higher yielding currency • Need an upward sloping YC, borrow short & lend long via three methods… 1. Borrow local bank, convert to higher rate Inter-Market Trade currency & invest in local high yield bond Buy 1yr MXP bond receive 7.28% 2. Currency swap – pay lower finance rates & receive higher rates 6mo GBP finance rate (0.47%) 3. Borrow in high rate currency & invest in = 6.81%/2 = 340.5 bps 6mo carry same country bond, then convert to lower Intra-market MXP trade no carry, flat YC yield currency position via forward market Inter-Market Trade Steep Alternatively Ride the NZD YC Buy 5yr NZD bond receive 2.92% curve • Steep slope for NZD, buy 5yr, roll down to 6mo GBP finance rate (0.47%)

4.5yr, yield pick up (2.92 – 2.84) = 8 bps Note: maturity mismatch = 2.45%/2 = 122.5 bps 6mo carry • Fixed rate swap leg MDur = 4.218 Ftn. 11 Market to market gain +33 bps • MDur x D yield pickup = 4.218 x 8 = 33 bps 155.50 bps 6mo carry • If YC moves up to reflect implied fwd. yield rises from 2.84% to 3.03%, 4.5yr swap yields rise 19 bps, resulting mark-to-market loss offsets carry accrual & pay 6mo NZD/receive 5yr NZD breaks-even EOC 25 Exh. 8 & 9 3/1/21 LevelUp, LLC©2021 All rights reserved 27

2. Volatile Yields in Unknown Direction?

• Susan Joenk – Bank PMgr. with IPS mandate Brazil’s yields are going to • Portfolio money duration = BM money duration 7.109 be volatile & unknown direction based on • BM = Bloomberg Emerging Mkt Sov. Bond Index election outcome …what • Sell 10yr. Brazilian bullet bond with duration = 7.109, should I do? convexity = 0.66 & YTM = 5.361% & buy barbell Exh. 21 Buy Brazilian 30-yr. Buy Brazilian 3-yr. vs.10yr. • Duration 2.895 • Duration 13.431Adding convexity0.66 • Convexity 0.105 & YTM 2.599% • Convexity 2.827 & YTM 6.332% BM Effective Duration= 3yr. note duration x% weight + 30yr. bond duration (1-x) %wgt 7.109 = 2.895x + 13.431(1 – x) Solve for x x = 0.60 or 60% in 3-yr. bond & remaining 40% in 30-yr. bond Buying 30yr. Bond ADDS Convexity During Volatility Weighted avg. of convexity purchased less convexity of bond sold Convexity Gain 0.528 = (60% x 0.105) + (40% x 2.827) – (100% x 0.66)

Yield Give-Up or ”Yield Drag” (-127 bps) Weighted average YTM purchased less YTM of bonds sold -1.268% = (60% x 2.599%) + (40% x 6.332%) – (100% x 5.361%)

Using Partials to Est. Portfolio Sensitivity YCD Exh 34 Case: Haskell Capital Management Forecast YC to Steepen • 2-10yr. yields fall 5bps • 30yr. yields rise 23 bps • Portfolio $60mm The “Boys” at Haskell Capital Mgt.

Less Less More More

2021 CFA errata Q20 x x solution add = negative sign

Predicted D = Portfolio par amount x partial PVBP x ( - Actual curve shift in bps)/100 Pro-forma 30yr. Predicted D = $60,000 x 0.0191 x (- 23/100) = -263.58 Smaller price drop Barbelled 30yr. Predicted D = $60,000 x 0.0238 x (- 23/100) = -328.44 Large price drop