Yield Curve Trade: Lamont Cranston Yield Income Rolldown Exp

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Fixed Income Portfolio Management (2)

Yield Curve Strategies

Inter (Outside) Market Convergence Trade Involves multiple YC’s & requires decision to accept or hedge currency risk Motivated by narrowing or widening yield spreads. Foreign position more attractive than domestic

German Insurance Co. anticipates economic 1. Buy 2yr vs. 10yr Greek Bonds growth & Greek yield spreads to tighten (rates fall) • 2yr. Greek bond is safer, shorter EUR yield curve to rise, which bond to purchase? maturity & duration, higher coupon • Greek 2yr. (4.75% coupon, price 99.18) 4.75% vs 3%, wider spread over • Greek 10yr. (3.00% coupon, price 78.86) German bonds & EUR swap rate 1. Buy 2yr. or 10yr. Greek bond outright, or… • 10yr Greek bond has higher yield 5.91%, longer duration provides 2. Asset swap = Buy GRK 10yr. Bond + pay fixed greater opportunity for yields to 3% timed to meet receipt of 3% coupon & receive tighten/narrow & earn inc. longer spread to 6mo floating rate, swap spread 220 bps Duration vs. Bond & YTM Exh 45 3 mo. 6 mo. 2 yr. 10 yr. 2. Asset Swap Spread Duration • EUR YC curve rising, don’t + Dur! Greek gov bond YTM 1.56% - 5.21% 5.91% Coupon 4.75% 3.00% • Benefit: (1) Greek spreads German Gov. Bonds -0.92% -0.72% -0.66% 0.43% narrow (prices rise :-) & (2) rising EUR swap rates spreads narrow Spread b/w bonds 5.87% 5.48% • Buy 10yr Greek bond (adds dur), EUR Swap -rising YC -0.33% -0.25% -0.15% 0.79% plus enter pay fixed/rec’v float, adds negative duration swap Spread b/w swap 5.36% 5.12% • Negative: pay 1.95% bps spread BBox 4 Michael Costos Life Ins Co. rec’v floating -0.25%, pay 2.20%) 3/2/21 LevelUp, LLC©2021 All rights reserved 4

Inter-Market Yield Curve Positioning Find most attractive cash-neutral & duration-neutral trade within each market

BBox 5 – Simon Millsap part I

Steps 1. Calculate the projected local currency returns (income/pull to par + rolldown + CM yield change) for each maturity and country 2. Identify the best pairwise total return trade (buy one maturity & sell another maturity) within the same currency pair 3. Calculate the duration change (add or subtract) for the best pairwise trade in #2 4. Calculate the opposite pairwise trade that neutralizes the duration change in step 3 5. Calculate the proportional reduction in one trade to match the dollar weights between the two pairwise trades

Inter-Market Yield Curve Positioning Find most attractive cash-neutral & duration-neutral trade within each market Assumptions 3 Return Sources • BM = developed sovereign bonds • Income – Bond coupon plus the change • Base USD, IPS prohibits short positions in price (P1-P0)/P0 from being pulled to par • Expects U.S. yields to rise & YC flatten, • Roll down return –the price change of a based on tight monetary policy, bond purchased today & held for 6 mo. • ECB & German rates to rise (prices fall) • Constant maturity yield D = projected • Yield spreads to widen uniformly change in yield as price pulled to par YC Observations Exh 47 Yields • U.S. higher yields @ every maturity, upward sloping YC, steep b/w 2s & 5s

Zero $ Cost & Duration Neutral Trade • Lend long & borrow short in one market Exh 50 • Lend short & borrow long in another mkt • Same maturities, different markets Identify Best Carry Trade • Steep Curve: Borrow short & lend long BBox 5 – Simon Millsap part I R17 Currency Sec 5.3 & 6.1.2 • Flat Curve: Lend short & borrow long EOC 26 3/2/21 LevelUp, LLC©2021 6

Components of Local Currency 6-mo. Returns Calculate Local Currency E(r) in 6 mo. = Income + Roll Down + Constant Maturity Yield D

Exh 47 & 51

Best US offers higher + Mkt. + = yields & income vs. UK & Germany

U.S. 5 yr. Note @ 1.90% Income return* = (Coupon + Priced @1.90%)/P0 - 1 • 2% coupon (1% for 6mo) 0.95% = (1.0% coupon + 100.4293)/100.4748 - 1

• Current Price P0 = 100.4748 *Income return includes both ½ yr. coupon + reduction in price since at a constant yield, the price is “pulled to par” as maturity shortens

P1 in 6mo with YC D Rolldown on a Stable YC (Aging) P1 100.4748 to yield 1.90% in 5yrs Rolldown = (Price @1.75% - [email protected]%)/Price0 Price with no change in yield 0.64% = (101.0773 - 100.4293)/100.4748 P1 @ 1.90% = 100.4293 in 4.5yrs Rolldown is the bond return purchased & held 6 mo. 1.75% = 1.90% - 0.15% rolldown 2021 CFA P1 @ 1.75% = 101.0773 (price up) Yields Change Equally Across the YC Errata 2.00% = 1.90% - 0.15% rolldown CM yield D = (Price @2.00% - [email protected]%)/Price0 + 0.25% YC D -1.07% = (100.0000 - 101.0773)/100.4748 P1 @ 2.00% = 100.00 (price falls) Exh 49 R18 Intro FI Sec 5 BBox 5 – Q1 3/2/21 LevelUp, LLC©2021 7

Components of Local Currency 6-mo. Returns US 5 yr. T-note, 2% coupon trading at premium 100.4748 with yields @ 1.90%

Premium Bond Pull to Par Rolldown or “Aging” CM Yield Change Maturity shortens 5yrs to Maturity shortens 5 to 4.5yrs Maturity constant @ 4.5yrs 4.5yrs, premium amortized Stable YC – No D in yields Yields expected to rise 25 No D in yields = 1.90% Yield adjusts from 1.90% @ bps from 1.75% to 2.0% Price falls from 100.4748 5yrs to 1.75% @ 4.5yrs Prices fall from 101.0773 to 100.4293 time shortens Prices rise from 100.4293 to to par 100 6 mo. income = 2%/2 = 1% 101.0773 (as yields fall)

= 1% + (100.4293/100.4748) -1 = (101.0773 – 100.4293/100.4748) = (100 – 101.0773/100.4748) = 0.01 + 0.9995 - 1 = 0.64% = -1.07% = 0.95% Total local 6 mo. return = 0.52% 100.4293 Price Yields Yields 100.0000 par 1.90% Yield @1.90 yield @2% yield 100.4748 “Riding the YC” “aging” 100.4293 2% Yield - Par 101.0774 101.0774 Yields now rise by 25 [email protected] yield @1.75 yield

Identify Barbell vs. Bullet Using Only CM Yield D Identify whether a barbell or bullet would be best among 2/5/10s & 5/10/30s • Considering only the constant maturity yield Exh 51 changes every market has a downward sloping flattening yield curve thus rising bond prices • Flattening YC - Long maturity bonds yields are falling greater than short yields & larger price incr. Dispersion!

• Barbell structures: 2s/5s, 5s/10s & 10s/30s • Longer maturity 10s & 30s bonds have the largest decrease in yield & largest price increases

• Longer barbell structure 2s/10s outperforms 5s bullet, provides great decrease in yield & therefore greater price increase • Longer 5s/30s barbell outperforms 10s bullet Falling yields = Rising prices BBox 5 – Q2

Best Pairwise Cash & Duration Neutral Trade Identify within each market the zero-cost trade (buy $1.0mm = sell $1.0mm) combo that increases return with no duration impact. Maximum position size +/- $1.0mm

US Pairwise Trades Returns from Exh 51 1. Calculate pairwise trade total return

Reduce duration trades Buy 5s/Sell 2s = 0.52 – 0.28 = 0.24% Buy 5s Increase duration trades Buy 5s Best Sell 2s Sell 30s Buy 5s/Sell 30s = 0.52 – (-1.37) = 1.89% pairwise trade

BUY Buy 10s Sell 30s Buy 10s/Sell 30s = - 0.05 – (-1.37) = +1.31%

MDur 2. Calculate D in duration for each pairwise trade Buy 5s/Sell 2s = 4.29 – 1.48 = 2.81 Buy 5s/Sell 30s = 4.29 – 11.69 = - 7.4 Both sell

Exh 48 Exh 30s reduce Buy 10s/Sell 30s = 8.42 – 11.69 = - 3.27 duration! Impact of MDur Duration values are treated as positive remove signs 3. Calculate pairwise trade return/D in MDur Buy 5s/Sell 2s = 0.24%/2.81 = 0.0854%

Buy 5s/Sell 30s = 1.89%/7.4 = 0.2554% Largest increase Buy 10s/Sell 30s = 1.31%/3.27 = 0.4037% per unit duration

Best Pairwise Intra-Market YC Trade - US Best Absolute Return US Mkt Pairwise Trade US Market Largest Return per unit of Duration Buy 5s/Sell 30s = 1.89% largest absolute Both Buy 10s/Sell 30s = 1.31%/3.27 = 0.4037% largest reduce return but reduces duration by 7.4 duration return per unit of duration, reduces duration 3.27 Identify an alternative duration neutral trade for each trade above to achieve duration (add) neutrality

Buy 10s/Sell 2s return = - 0.33% Buy 5s/Sell 2s return = + 0.24% 8.42 – 1.48 = 6.94 increases duration 4.29 – 1.48 = 2.81 increases duration • Increases duration but not enough to • Cannot buy more than $1.0 trade size offset the buy 5s/sell 30s 7.4 position Both trades to increase duration towards 3.27 increase • Trade size again limited to 1.0mm so duration but we cannot increase duration by not enough Use a ratio of the two duration purchasing more than $1.0mm positions to reduce the Buy 10s/Sell 30s trade size Use a ratio of the two duration positions 2.81/3.27 = 0.8593% to reduce Buy 5s/Sell 30s trade size 6.94/7.4 = 0.9378%, the new $ position of Return = (1.31% x 0.8593) + 0.24 = 1.3567% *Buy 5s/Sell 30s = $0.9378mm Increase in return for this pairwise intra- Errata* market trade Return = (1.89% x 0.9378) – 0.33 = 1.4424%

Best US Intra Market Trade Now repeat for UK & Germany! US Market Buy 5s & 10s US Market Sell 2s & 30s BBox 5 – Q3

Best Pairwise Intra-Market YC Trade- UK

$1.0mm buy = $1.0mm sale Best pairwise trade returns 2s returns all stink from buying 5s & 10s and selling 2s & 30s 30s returns stink too

Both trades Buy 5s/Sell 30s = + 0.29% Buy 10s/Sell 30s = + 0.79% reduces Reduces duration: 4.44 – 12.75 = - 8.31 duration Reduces duration: 9.03 – 12.75 = - 3.72 Identify duration neutral trade for each trade above

Buy 10s/Sell 2s = + 0.85% This trade Buy 5s/Sell 2s = + 0.35% increases Increases duration 9.03 – 1.50 = 7.53 but Increases duration 4.44 – 1.50 = 2.94 but not enough to offset the Buy 5s/Sell 30s duration by not enough to offset the Buy 10s/Sell 30s buying the longer Reduce Buy 5s/Sell 30s trade size by Reduce Buy 10s/Sell 30s trade size by 7.53/8.31 = 0.9061% of $1.0mm duration 2.94/3.72 = 0.7903% of $1.0mm bond New $ position Buy5s/Sell 30s = $0.9061mm New $ position Buy 10s/Sell 30s = $0.7903mm

Return = (0.29% x 0.9061) + 0.85% = 1.1128% Return = (0.79% x 0.7903%) + 0.35% = 0.9744% Best UK Intra Market Trade UK Market Buy 5s & 10s Exh 51 Exh 48 Durations BBox 5 – Q3 UK Market Sell 2s & 30s 3/2/21 LevelUp, LLC©2021 12

Best Pairwise Intra-Market YC Trade - Germany

$1.0mm buy = $1.0mm sale

Best pairwise trade returns 5s all stink from buying 30s & 2s & 10s ok – selling 5s & 10s 30s better

Buy 30s/Sell 5s = + 3.21% Initial trade Buy 30s/Sell 10s = + 1.33% increase Increases duration: 13.22 – 4.48 = + 8.74 Increases duration: 13.22 – 9.27 = +3.95 duration Identify duration neutral trade for each trade above Buy 2s/Sell 10s = - 0.81% This trade Buy 2s/Sell 5s = + 1.07% Reduces duration 1.50 - 9.27 = -7.77 but decreases Reduces duration 1.50 – 4.48 = - 2.98 but not enough to offset Buy 30s/Sell 5s duration by not enough to offset the Buy 30s/Sell 10s selling the Reduce Buy 30s/Sell 5s trade size longer Reduce Buy 30s/Sell 10s trade size 2.98/3.95 7.77/8.74 = 0.8890% of $1.0mm duration = 0.7544% of $1.0mm New $ position buy30s/sell 5s = $0.8890mm bond New $ position buy 30s/sell 10s = $0.7544mm

Return = (3.21% x 0.8890) – 0.81% = 2.0437% Return = (1.33% x 0.7544%) + 1.07% = 2.07% Best German Intra Market Trade German Market Buy 2s & 30s BBox 5 – Q3 Exh 48 Durations German Market Sell 5s & 10s 3/2/21 LevelUp, LLC©2021 13

Identify Best Cash & Duration Neutral Trade • Local currency (LC) bond returns are NOT comparable unless the FX currency is hedged • Hedge UK & German returns to USD by selling FX forward to hedge initial long position (below) • Constrain maximum position for any bond = +/- $1.0mm • Use each market (US, UK, German) best buys = US 5s, German 10s & UK30s (below) • At each maturity look for all inter-market trades (next slide) that increase return • Calculate net trade duration (1.39 next slide) at each maturity & then look for a trade across maturities that is duration neutral but increases returns (our ultimate objective) German LC + FX Hedged Exh 50 Bonds Return Return = Return Contango* 2yr -1.51% 0.85% -0.66% Contango* 5yr -2.58% 0.85% -1.73%

* Both markets are in Contango F>S, selling the forward short earns a profit 10yr -0.70% 0.85% 0.15% • Buy EUR spot 1.0998 & sell 6-mo forward 1.1091 30yr 0.63% 0.85% 1.48% • FX return = P1/P0 - 1 = (1.1091/1.0998) – 1 = + 0.85% UK LC + FX Hedged Bonds Return Return = Return • Buy GBP spot 1.2982 & sell 6-mo forward 1.3045 2yr -0.30% 0.49% 0.19% • FX return = P1/P0 - 1 = (1.3045/1.2982) – 1 = + 0.49% Hedging both UK & German markets result in positive returns 5yr 0.05% 0.49% 0.54% US Bonds 2yr. 5yr 10yr 30yr 10yr 0.55% 0.49% 1.04% LC Return 0.28% 0.52% -0.05% -1.37% 30yr -0.24% 0.49% 0.25% BBox 5 – Q4 & Q5 Exh 51 LC Bond Returns Exh 52 Hedged Bond Returns 3/2/21 LevelUp, LLC©2021 14

Flip Flop Exh 51 Best intra- Pairwise Best Trade Pairwise Best Trade Pairwise Best Trade market unhedged • Buy 5s +0.52% & 10s (-0.05%) • Buy 5s & 10s • Buy 2s (-1.51%) & 30s +0.63% return trades • Sell 2s +0.28 & 30s (-1.37%) • Sell 2s & 30s • Sell 5s (-2.58%) & 10s -0.70%

2s & 10s switch 2s & 10s switch Best inter- Pairwise Best Trade Pairwise Best Trade Pairwise Best Trade market • Buy 2s (+0.28%) • Buy 5s & 10s • Buy 10s (0.15%) Exh 53 hedged • Sell 10s (-0.05%) • Sell 2s & 30s • Sell 2s (-0.66%) return trades

A $1.0mm par purchase & sell of each bond results in cash-neutral Exh. 48 Mod Durations trade but not a duration-neutral trade Net duration impact of the From LC hedged returns above, optimize across all maturities best bond to twelve trades = -1.52 + buy/sell while keeping $1.0mm trade & calculate the net duration impact 4.25 + 9.88 – 11.22 = 1.39 • Buy US 2s 1.48 - Sell UK 2s 1.50 - Sell German 2s 1.50 = -1.52 Need to reduce duration • Buy US 5s 4.29 + Buy UK 5s 4.44 - Sell German 5s 4.48 = +4.25 back to neutrality, reduce • Sell US 10s -8.42 + Buy UK 10s 9.03 + Buy German 10s 9.27 = +9.88 duration using long bonds (German 10s +0.15% and • Sell US 30s -11.69 - Sell UK 30s 12.75 + Buy German 30s 13.22 = -11.22 30s 1.48% & UK 10s 1.04%)

R20 YC Strategies EOC#26 Considering only the US, UK & Euro markets, the most attractive duration neutral, currency neutral carry-trade could be implemented as: Duration Neutral & Currency Neutral Carry-trade Basics 1. Identify the steepest yield curve (within same market) 2. Steep curve: borrow short & lend long (U.K. market) 3. Flat curve: Lend short & borrow long 6mo Fixed Rates with Semi-annual Payments 3yr - Exh 1 Floating 1 Yr. 2 Yr. 3 Yr. 6mo 4 Yr. 5 Yr. Euro 0.15% 0.25% 0.30% 0.40% +0.25% 0.50% 0.60% Flattest U.K. 0.50% 0.70% 0.80% 0.95% +0.45% 1.00% 1.10% Steepest U.S. 1.40% 1.55% 1.70% 1.80% 0.40% 1.90% 1.95% Buy 3yr. UK Gilts & Sell 3yr Euro notes & enter 6mo forward FX pay Euro/receive GBP Swap = UK receive 3yr. fixed & pay 6mo. float + Euro receive 6mo. float & pay 3yr. fixed • Receive U.K. 3yr fixed +0.95 & pay 6mo float - 0.50% = +0.45% Net carry = 0.20% • Pay Euro 3yr fixed - 0.40% & receive 6mo. float 0.15% = -0.25% or 0.10% for 6mo Long 5yr US T-note futures & sell 5yr Euro (German) note futures for delivery in 6mo. US carry = (1.95% - 1.40%)/2 = 0.275% Euro carry = (-0.60% + 0.15%)/2 = -0.225% 3/2/21 LevelUp, LLC© 2021 All rights reserved Net carry = 0.05% 16

R20 YC Strategies EOC#27 If Winslow is limited to unhedged positions or hedging into each portfolio’s base currency, she can obtain the highest expected returns by:

Hedged Return = Local Currency Unhedged Return – Hedging Cost

Winslow’s Market Outlook 1. Stable yields in US, Euro, UK & Greek markets Steps 2. Mexico yields to decline to 7% at all maturities 1. Solve for local market return 3. Mexican Peso to depreciate 2% vs. Euro 2. Solve for cost of hedge 4. USD to depreciate 1% vs. Euro 3. Identify best trade 5. GBP remain stable vs. Euro

6mo Fixed Rates with Semi-annual Payments Exh 1 Floating 1 Yr. 2 Yr. 3 Yr. 4 Yr. 5 Yr. Mexico 7.10% 7.15% 7.20% 7.25% 7.25% 7.25% Greece - 3.30% 5.65% 5.65% 5.70% 5.70% Euro 0.15% 0.25% 0.30% 0.40% 0.50% 0.60% U.K. 0.50% 0.70% 0.80% 0.95% 1.00% 1.10% U.S. 1.40% 1.55% 1.70% 1.80% 1.90% 1.95%

R20 YC Strategies EOC#27 Winslow’s Market Outlook Solve for the 6 month 1. Stable yields in Greek, Euro, UK & US markets local currency return 2. Mexico yields to decline to 7% at all maturities

Mexico 5 yr. priced to yield 7% (yields fall, prices rise) over next 6 months n = 4.5 yrs. x 2 = 9 Local currency return = (P + Coupon/2)/P i = 7% yield/2 = 3.5% 1 0 4.576% = (100.9501 + 7.25/2)/100 - 1 FV = 100 par Pmt = (100 x 7.25%)/2 = 3.625

Solve for price1 (PV) = 100.9501

6mo Fixed Rates with Semi-annual Payments 6 mo LC return = Exh 1 Floating 1 Yr. 2 Yr. 3 Yr. 4 Yr. 5 Yr. ½ coupon Mexico 7.10% 7.15% 7.20% 7.25% 7.25% 7.25% 4.576% Greece - 3.30% 5.65% 5.65% 5.70% 5.70% x ½ = 2.85% Euro 0.15% 0.25% 0.30% 0.40% 0.50% 0.60% x ½ = 0.30% U.K. 0.50% 0.70% 0.80% 0.95% 1.00% 1.10% x ½ = 0.55% U.S. 1.40% 1.55% 1.70% 1.80% 1.90% 1.95% x ½ = 0.975%

R20 YC Strategies EOC#27 Hedging Cost = 6mo rate hedged bond – 6mo rate for the currency in which the bond is denom Hedge Cost 6mo Hedged Bond – Denom Currency Bond 6 mo

MXP into Euros (0.15% - 7.10%) = - 6.95%/2 = - 3.475%

GBP into Euros (0.15% - 0.50%) = - 0.35/2 = - 0.175% USD into Euros (0.15% - 1.40%) = - 1.25/2 = - 0.625%

Local mkt 6mo return Hedging Cost Hedged Return € Mexico 4.576% - 3.475% 1.101% = Greece 2.850% 0 2.850% = Euro 0.300% 0 0.300% = U.K. 0.550% - 0.175% 0.375% = U.S. 0.975% - 0.625% 0.350% Buy Mex 5yr. & hedge into base currency of the portfolio – 5yr Greek > 5yr Mex

Buy Greek 5yr. 2.850% & hedge GBP (stable FX) & leave unhedged in USD 1.850%

R20 YC Strategies EOC#28 Hedging Cost = 6mo rate hedged bond – 6mo rate for the currency in which the bond is denom Hedge Cost 6mo Hedged Bond – Denom Currency Bond 6 mo

MXP into Euros (0.15% - 7.10%) = - 6.95%/2 = - 3.475% Winslow is allowed to GBP into Euros (0.15% - 0.50%) = - 0.35/2 = - 0.175% hedge into any currency, her highest USD into Euros (0.15% - 1.40%) = - 1.25/2 = - 0.625% expected return is…? Local mkt 6mo return Hedging Cost Hedged Return € Mexico 4.576% - 3.475% = 1.101% Greece 2.850% 0 = 2.850%

1. Mexican Peso to depreciate 2% vs. Euro 2. USD to depreciate 1% vs. Euro 3. GBP remain stable vs. Euro Buy 5yr Greek 2.85% in each portfolio & hedge into Pesos – not hedge into euros +3.475 (benefit) less peso depreciation -2.0% = +1.475% currency return = 4.325% Buy 5yr Greek 2.85% in each portfolio & hedge into USD costs 0.625% = 2.225% Buy 5yr Greek 2.85% in each portfolio & not hedge the currency = 2.850% 3/2/21 LevelUp, LLC© 2021 All rights reserved 20

Yield Curve Trade: Lamont Cranston Yield Income Rolldown Exp. D in yields & yield spreads Exp. Annual coupon (Price1 – Price0) = [- MD x ∆ yield] + [½ x Convexity x ( ∆ yield)2] return + + Current bond price Price0 Or effective duration & convexity at horizon date

I prefer “barbells” as they roll down an Bullet 5yr = [ - 3.98 x 0.005] + [½ x 17.82 x (0.005)2] = -1.9677% upward sloping YC “The Shadow”

Barbell 2s/10s= [ - 3.98 x 0.005] + [½ x 32.57 x (0.005)2] = -1.9493% R18 Intro FI Sec 5.1 * Recall higher convexity slightly outperforms in a parallel move YC shift upward by 50 bps Bullet Barbell Stable YC Bullet Barbell Portfolio – Zero Coupon Bonds 5s 2s & 10s Yield 0% 0% Investment horizon yrs. 1 yr 1 yr + Rolldown 1.598% 1.844% +25 EOC 13 Avg. Current Price – P 94.5392 92.6437 0 +/-D Yields -1.968% -1.949% +2 Avg. Price in 1 yr – stable YC 96.0503 94.3525 E(r) -0.369% -0.105% +26 Modified Duration - now 4.97 4.93 Barbell outperforms Bullet Exp. Effective Duration in 1 yr 3.98 3.98 • 10yr zero price appreciation is Exp. Convexity @ horizon date 17.82 32.57 greater than 5 yr zero as they “ride Exp. D in US Treasury Zero YC 0.50% 0.50% the yield curve” to a shorter maturity Exh 70-71 BBox 7 EOC 14 3/2/21 LevelUp, LLC©2021 All rights reserved 21

Fixed Income Portfolio Management (2)

Credit Strategies

BM & G-Spread - Hedging IR Risk Credit Spread = fn(likelihood of default & probable loss, credit migration & mkt liquidity risk) Benchmark Credit Spread = Credit security yield – On-the-run, risk-free gov. bond yield Maturity mismatch b/w credit security & BM bond, requires BM yield curve to be flat

G Spread = Credit bond yield – linear interpolation b/w 2 gov. bond OTR yields Weighted avg. gov. bond maturity to credit bond maturity

March 2016 (on-the-run gov. bonds) Price Yield Maturity Eff Dur No Citigroup 3.75% due June 2024 optionality 103.64 3.24% 7.96 7.0 US Treasury 1.5% due March 2023 (7yr) 99.80 1.53% 7.00 6.7 1.63% US Treasury 1.625% due Feb 2026 (10yr) 98.70 1.77% 9.88 9.1

1. Maturity weighting 7.96 = 7.0x + 9.88(1-x), x = 66.7% weight in 7yr & 33.3% in 10yr 2. Linear interpolated yield: 1.61% = (66.7% x 1.53%) + (33.3% x 1.77%) no D in yields 3. G-spread on Citi bond: 1.63% = 3.24% – 1.61% Yields fall 7 bps on the 7-yr Treasury from 1.53% to 1.43%, no change in 10-yr yields 4. New Treasury interpolated yield after yield change: 1.54% = (66.7% x 1.43%) + (33.3% x 1.77%) 5. Determine the new Citi yield after 7 bps yield change = 1.54% + 1.63% = 3.17% 6. Calc new Citi price when yields fall by 7 bps: 103.64 x [1 + (- 7 x - 0.07%)] = 104.15 To hedge IR risk credit bond, sell duration weighted 87.5%-7yr & 12.5%-10yr gov bonds EOC 10 BBoxes 2 & 8 part 2 3/2/21 LevelUp, LLC©2021 All rights reserved 23

I, Z & OAS Relative Value Spreads Used to Hedge & Price Measure Relative Values I-Spread (Interpolated) Z-Spread (Zero-Volatility) • I- Spread = credit security yield - • Amount of yield from a non-Treasury bond swap rate yields denominated in above the yield for the same maturity same currency as the credit security Treasury bond, requires PV of CFs BBox 8 Q2 Exh 5 • For bonds w/o embedded options it is a I-Spread Advantage good measure of a bond’s credit spread • Smoother swap curves vs. government yield curves • I & G spread are useful in pricing & hedging credit securities Call option value 74 = 371 Z spread – 297 OAS G & I Spread Key Points OAS Spread BBoxes 3* & 4* 1.The BM rate is most helpful when • Call option value = Z spread – OAS spread risk-free. If the BM has credit risk, • Best relative value spread measure for then gov. bond yields will not be a embedded option bonds & portfolios good choices for a risk-free BM • Add OAS to all one-period forward rates to 2.If hedging interest rate exposure set an arbitrage-free bond equal to MV use the I-spread but use government bond yields instead of • Requires assumptions about IR volatility swap rates, then realized spread ≠ • Realized spread < or > OAS spread calculated spread • OAS is a theoretical credit spread measure 3/2/21 LevelUp, LLC©2021 All rights reserved EOC 3 24

EXcess Return - XR Excess (credit risk) return = Credit bond return – hedged interest rate risk

*t expressed in fraction of year XRNoDefaultLoss ≈(s x t*) – (Ds x SD)

(SpreadBeg x Holding Period) – (Change in Spread x Spread Duration) Unknown in advance EXR ≈(s x t) – (Ds x SD) – (t x p x L) Eq. 1 & 2 DefaultLoss Exp. Credit Loss Annualized Expected – (Holding Period x Prob. Default x Loss Severity)

Excess Return Example Credit Spread Narrows 50 bps held 6 months • Corporate bond XR = (2.75% x 1/2) – [(2.25% – 2.75%) x 5] • Spread duration 5 yrs. XR = 1.375% – (– 2.5%) = 3.875% (prices rise) • Current credit spread 2.75% Instantaneous Credit Spread Rises 50 bps • 1% Annualized prob. of default XR = (2.75% x 0) – [(3.25% – 2.75%) x 5] • Expected loss severity 60% XR = 0 – (2.5%) = – 2.5% (prices fall) Credit Spread Narrows 50 bps, held 6 months with Default Probability EXR = (2.75% x 1/2) – [(2.25% – 2.75%) x 5] – (1/2 x 1% x 60%) EXR = 1.375% – (– 2.5%) – 0.3% = 3.575% BBoxes 5 & 7 3/2/21 LevelUp, LLC©2021 All rights reserved 25

4 Bottom Up Credit Strategies Exh. 6 3. Spread Curves Comparison • Same company bonds with different maturity & duration • Curve of fitted credit spreads • Compare bonds with similar coupons, credit ratings, issue size (liquidity), credit spread & price, watch levels of seniority

Bond Coupon Maturity Credit Issue Duration Price Yield Credit Spread

D 3.50% 5 yrs. A2/A 1.5 bn 4.6 100 3.50% 50 bps

E 4.00% 10 A2/A 3.0 bn 8.2 100 4.00% 80 bps

F 5.00% 30 A2/A 1.0 bn 15.8 100 5.00% 100bps

Interpolated Spread - Example • Explain, using relative value analysis, how the new issue bond E compares with outstanding bonds D & F? • Solve for weights using duration 8.2 = 4.6x + 15.8(1-x), D = 67.85% & F = 32.14% • Solve for Interpolated spread 66 = (67.85% x 50) + (32.14% x 100) • New issue E spread of 80 is attractive (wider spread 80 = lower price) vs. interpolated spread of 66 (narrower spread & higher price) • Short cut method 66 = 50 + {[(8.2 – 4.6)/(15.8 – 4.6)] x (100 – 50)} (next slide)

Interpolated Spread Short Cut Method Credit Spread (bps)

100 ------

X ------

50 ------Duration 4.6 8.2 15.8 X = 50 + [(100 – 50) x (8.2 – 4.6)/(15.8 – 4.6)] X = 50 + [50 x 3.6/11.2] X = 50 + 16.07 X = 66 see prior slide

EXcess Returns - Top-Down Credit Example Credit Current Expected Expected Credit Spread Rating OAS in OAS in 1 yr. Loss Rate Duration (SD) Category bps (s) in bps = (p x L) Assume no D A 244 118 0.00% 5.6

Baa 334 206 0.04% 6.1

Ba 571 370 0.08% 4.4

B 736 510 0.31% 3.9 Spreads Narrowing Spreads

Eq. 2 EXRDefaultLoss ≈(s x t*) – (Ds x SD) – (t* x p x L) Trade off: Higher EXR vs. Ds = OAS in 1 yr. – OAS today more volatile & less liquid

Calculate EXRDefaultLoss Assuming No Change in Spread Duration A EXR ≈ (0.0244 x 1) – [(0.0118 – 0.0244) x 5.6] – (1 x 0) = 0.095 or 9.5% Baa EXR ≈ (0.0334 x 1) – [(0.0206 – 0.0344) x 6.1] – (1 x 0.0004) = 0.111 or 11.1% Ba EXR ≈ (0.0571 x 1) – [(0.037 – 0.0571) x 4.4] – (1 x 0.0008) = 0.1447 or 14.5% B EXR ≈ (0.0736 x 1) – [(0.051 – 0.0736) x 3.9] – (1 x 0.0031) = 0.1586 or 15.9% Lower rated credit bonds Ba & B will outperform higher credit rated bonds A & Baa