EFTA01077898.pdf

Deutsche Bank Markets Research VA North America Derivatives S' Date United States 3 December 2013 US Derivatives Spotlight Sau l Agganval The Compelling Case for Long-Dated SPX Calls The current combination of low volatility levels and embedded protection makes longer-dated call strategies attractive to position for further equity appreciation. With call premia near decade-long lows, upside options offer benefits compared to long equity positions or can be used to safely enhance core cash equity holdings. In this note we examine the pricing drivers of SPX 18- to 36-month expiry call options and compare historical returns of different strategies and to outright equity. Broadly, call strategies have exhibited better risk-adjusted returns than holding a cash position in the SPX index. Long-dated calls on the SPX index are priced attractively There are two main drivers of long-dated call premia, both of which help make pricing compelling right now • Long-dated SPX spot implied volatility is extremely low. The depressed rates volatility and low correlation between rates and equities create further downward pressure on the implied volatility of the SPX forward • The SPX forward itself is depressed vs. the spot level. The currently low level of interest rates and relatively high implied dividend yields have resulted in negative carry costs and have pressured the SPX forward, which makes the option premia appear low optically Choosing a long-dated call strategy: findings from our 10-year backtest • We find that call spreads tended to have the highest risk-adjusted returns among the strategies studied. • Strategies involving selling 1M options to finance the longer-dated calls have performed better than equity and outright calls. These results are consistent with our previous research showing that implied volatility risk- premium is typically rich for short-dated options. However, short 1M options underperform in strongly rallying markets, such as the SPX this year. • Rolling a long call (spread) position before expiry would have generally (but not always) resulted in higher risk-adjusted returns. Rolling prior to expiry reduces the negative effects of time decay, since shorter-dated options lose time value quickly Sensitivity of call premia and relative magnitude of risks While delta is the main driver of call P/L longer-dated options have a higher exposure to other risks. We compare the impact on current SPX call premium from changes in spot, time, implied volatility, rates, and dividend yields. Risks headline The loss from a long option or long option spread position is limited to the net premium paid. Please note that hypothetical backtest results are neither an indicator nor a guarantee of future returns. Deutsche Bank Securities Inc. Note to U.S. investors: US regulators have not approved most foreign listed stock index futures and options for US investors. Eligible investors may be able to get exposure through over-the-counter products. Deutsche Bank does and seeks to do business with companies covered in its research reports. Thus, investors should be aware that the firm may have a conflict of interest that could affect the objectivity of this report. Investors should consider this report as only a single factor in making their investment decision. DISCLOSURES AND ANALYST CERTIFICATIONS ARE LOCATED IN APPENDIX 1.MICA(P) 054/04/2013. EFTA01077898 3 December 2013 US Derivatives Spotlight The basics of long-dated calls Better risk-adjusted returns at an attractive price Buying long-dated call options offers benefits to investors seeking equity exposure. They allow for continued upside participation and at the same time provide a floor should the broad market decline rapidly. In this note, we show that longer-dated SPX call strategies have historically provided better risk- adjusted returns compared with buying and holding the broad index. There are several key features of call options that should appeal to a wide range of equity investors: • Current pricing: Long-dated calls on the SPX index are priced attractively with levels for both ATM and OTM calls near decade-long lows (see Figure 1) • Embedded risk management characteristics: Call 'delta' (sensitivity of the call's price to spot moves) increases in a rally and decreases in a sell-off. Thus investors get longer as the market moves higher and less long as the market sells off. This convexity property of long options is especially attractive in a market pullback and is a reason why long-dated calls result in higher risk-adjusted returns in our backtests vs long equity only Figure 1: Current long-dated call option premium near decade-long lows 30% 25% 20% 15% 3 10% 5% 0% Jan-03 Jan-05 Jan-07 Jan-09 Jan-11 Jan-13 Sage* ox•ale Batt The note is divided into three parts: • Why current pricing on long-dated calls is attractive relative to history • How different long-dated call structures have performed historically, including partly cheapening long-dated calls by selling higher strike calls with the same maturity and by selling 1M calls • What is the relative magnitude of the different risks inherent in long call positions Page 2 Deutsche Bank Securities Inc. EFTA01077899 3 December 2013 US Derivatives Spotlight Low rates, high dividend yields, and low implied volatility levels make long-dated calls historically cheap Figure 2 shows the drivers of call option pricing, which are now at levels that make current pricing attractive. The colors signify whether these values are low (green) or high (red) within their history since Jan-03. We also annotate the boxes if higher values of these factors affect call premia positively ('+') or negatively ('—'). For example, dividend yields are currently high from a historical perspective (red) and increasing yields would lead to lower call premia ('—' sign). Thus we can infer from the figure that the currently elevated dividend yields help lower call premia. Most of these drivers of long-dated call prices are addressed below. Figure 2: Low vol, low rates, and high implied dividend yields depress call premia' Spot Volatility Strike (+) Rate Vo latility I+) Dividend Yield L otatility (+) i Call Premia Forward/Spot I+) ;Ill (-) Others* (+) Vibes netidai cOndand veafW. ten vounMy aNe sax iweitno.ertmr L Tenor Repo (-) Saectv Deutsch, ea.* Figure 3 shows the distribution of call pricing for different maturities and strikes over the past ten years. As you can see current pricing for these calls strategies is near the bottom of its range over the past decade. It is particularly notable that levels are near lows for the range of maturities and strikes. 1 The boxes are cedar coded depending on the percentie rank of current values ccenpared with their histories over the past eight years. Green color is for a low percentile rank and red is for high. Deutsche Bank Securities Inc. Page 3 EFTA01077900 3 December 2013 US Derivatives Spotlight Figure 3: Current premia for long-dated SPX calls and call spreads is low 35% • Current Premia 30% - 25% 20% i? t 15% - 10% - 5% - 0% SPX 18M SPX 36M SPX 60M SPX 18M SPX 36M SPX 60M SPX 60N1 100% 100% 100% 107.5% 120% 140% 100%-140% Scance. Axascht Bane &tit .I.An Aron 'WOW( th) ckvance &Waxy,et. murmur,' encimoonwn of me CAA OPeOP. permti veva Jon-2003 en N 1O tois egworan• SN, thstnce bolvrtnv, 160— 260 IltrOMIAN 01the co: opt, perms MX'S .An-1002 The Me a -ewe°, m0 POlow MS fepretere tAt medal. aW won prow we am.2003 Sokldons TWORNIf the currentlevelal Sy in:have The main driver of the depressed option premium is due to SPX spot implied which has declined sharply throughout 2013 (see Figure 4). Further downward pressure on SPX long-dated call premia is also due to low rate volatility and the decreased correlation between rates and equities (longer maturity equates to greater sensitivity to the volatility of the forward vs. short-dated options, see Figure 5). Figure 4: SPX long-dated ATMS implied vols are near historically low levels... 50% ( Figure 5: ...as are rate implied volatility and rate-equity correlations* 250 45% 200 40% 150 35% 100 30% 50 25% 0 -50 — 3M ATMF implied volatility for 5Y swaption -100 — 3M realized correlation between 5Y rates and SPX May-05 May-07 May-09 May-11 May-13 Sault*. Deuesehe &ea Sweet ilkatere &ea 8 ,00M0011) Paws LP - WO MOMMOMS 00rnitISM at a NOW ke ArnOtd ON to data unatatlgiby A second effect is due to the SPX forward itself which is materially lower vs. the spot level. This makes the SPX option premia appear low optically. The following equations help understand the drivers of the forward: Forward = Spot + Cost of Carry Cost of Carry = Spot x (Interest Rate - Repo - Dividend Yield) x Time Page 4 Deutsche Bank Securities Inc. EFTA01077901 3 December 2013 US Derivatives Spotlight US interest rates have been depressed by the iterations of QE programs and dividend payments have been increasing in the post financial crisis recovery. The low level of rates (see Figure 6) and relatively high implied dividend yields (see Figure 7) have resulted in negative carry costs and have reduced the SPX forward (the spot value 'grown' by the carrying costs, see Figure 8). Please note that the effect of the forward on the call premia is 'optics' - dividends will reduce the price of the underlying (and call options as well if actual dividends are higher than priced into options). However, as shown in Figure 2, rates rising from these low levels and/or dividend yields falling will result in a mark-to-market gain on the long call position, all else equal. Figure 6: Low rates... Figure 7: ...and relatively high SPX implied dividend yields... 6% 3.0% 2.8% —36M 5% 2.6% —60M 4% 2.4% 3% 2.2% 2.0% 2% 1.8% —36M US Swap Rate 1% —60M US Swap Rate 1.6% 0% 1.4% Jan-03 Jan-05 Jan-07 Jan-09 Jan-11 Jan-13 Jan-03 Jan-05 Jan-07 Jan-09 Jan-11 Jan-13 Source: Asset Bet. Blositiknntaut LP I Swett Dame/* &sit IFigure 8: ...have depressed SPX forward levels 120% — 36M SPX Forward/Spot 115% — 60M SPX Forward/Spot 110% 105% 100% 95% 90% Jan-03 Jan-05 Jan-07 Jan-09 Jan-11 Jan-13 Sae= Deutsche Sent Anecdotally, a less material impact on SPX call premia is due to repo rates which decreased significantly at the beginning of 2013 and have rebased to a much lower range since then. The lower repo level and elevated repo volatility are factors that have pushed call prices slightly higher from where they would otherwise be. Deutsche Bank Securities Inc. Page 5 EFTA01077902 3 December 2013 US Derivatives Spotlight The low forward combined with depressed long-dated implied volatility has resulted in the most attractive pricing on long-dated call options in many years. As an example of how marked this difference can be, if we compare prices of 60-month maturity SPX ATMS calls on 30-Jun-03 and 11.Oct-13, two periods with the same implied volatilities but very different forwards, the difference in premium is —4.5% (19.1% vs. 14.6%). However, if we compare the option prices in terms of the forward (ATMF strikes), then the above mentioned spread in the premium disappears. Historical performance of long-dated calls Option strategies have had better risk-adjusted returns vs index performance In this section, we look at the historical performance of different long-dated call strategies?. We compare the performance of the option positions vs. the total return on the SPX Index. These backtests3 focus on SPX 18M and 36M options. We chose the 18M maturity for our backtests since many investors prefer exchange-listed options to OTC and 18M is the farthest listed maturity for which we had consistent data for the SPX. We chose the 36M maturity to study the results for even longer-dated options whose vega exposure does not decay as rapidly. Our results are largely similar among the two maturities studied and include those for • Calls and call spreads either held to maturity or rolled° after some time has passed in the life of the option • Call diagonals (buy long-dated calls financed by selling 1M calls) where the long-dated call is either held to maturity or rolled after some time has passed in the life of the option We find that: • Call spreads tend to have the highest risk-adjusted return, even after scaling their delta higher to match the initial delta of just the long call leg • Selling 1M 2% annualized premia calls to finance the purchase of long-dated calls has had better risk-adjusted performance compared with equity or outright calls • Rolling long-dated calls and call spreads prior to expiry has generally (but not always) resulted in higher risk-adjusted returns than holding them to expiry The table below displays the performance of these strategies in up and down market periods. The option strategies have tended to suffer less during market downturns but have underperformed in rising markets. This is expected as call options have a delta of less than 1- for every $1 change in the SPX, the call price will change by less than 1 (by their delta value to be exact), all else equal. 2 8acktests are for the Dec-02 to Sep-13 period. We assume a transactions cost of 0.30 vols for outright long dated calls and for those calls financed by selling 1M puts. In addition, we assume that the 1M options are sold at the bid. We assume a transaction cost of 0.20 vols for call spreads, which is applied to the closer-to-the-money strike. M an example, it the 18M ATM call has a vega or volatility sensitivity of 4, then we add 0.3x4=S1.2 to the mid ATM call price as transaction cost. 3 The backtests below assume that a long investor replaces his long delta-one position with an equivalent notional of calls (that is 1 outright call or spread contract per 1CO 'shares' in the index). All excess tunds are invested in short-term Treasury securities. 4 We roll the long-dated calks after lard and 2i3rds of the option's time has passed. Page 6 Deutsche Bank Securities Inc. EFTA01077903 3 December 2013 US Derivatives Spotlight Figure 9: Comparing performance under rising and falling markets: Equity vs. various 36M call option strategies rolled after 24M Dna to Oft4/7 Oats Is. IlMr•011to Sopli Apra to Septa Bake to Sett Return Volatility Return Volatility Return Volatility Return Volatiety Pattern VolatlAy RatNol EMMY 133% 128% 663% 376% 22.3% 18.7% MS% 11.3% 80% 203% 39.2% Outright ATM 83% 10.4% .220% 11.7% 10.3% 11.4% 13.6% 7.9% 6.1% 44.2% 89rWak AIM -8% 5,8% 50% -113% 6.7% 11% 7.5% 4.5% 2.0% 4.5% 13,4% 70,1% 89rWak AIM - 2% 7.9% 86% -18.1% 9.8% 10.1% 10.3% 10.1% 5.2% 53% 9.5% 55.8% Spread: ATM • 1/4 2% 9.1% 96% .20.1% 113% 98% 106% % 7.1% 6.5% 10.2% 63.6% $a ca'' Anon.. (Pant ['bomber'Para, LP Since the total return (price appreciation + dividends) on the SPX has been positive over the period studied (Dec-02 to Sep-13), the options strategies5 studied have underperformed the SPX (see Figure 10). However, after adjusting retums by the level of realized volatility (return/realized volatility) for the entire period, the option strategies had better performance when compared with equity°. The lower portfolio volatility of the call strategies is a key attraction for investors who are seeking equity returns but are put off by the typically high volatility of equity portfolios. Figure 10: Comparing performance of equity with various 36M calls rolled after 24M 260 — Equity 240 Outright: ATM Spread: ATM - 6% 220 — Spread: ATM - 2% 200 —Spread: ATM - 1M 2% 180 160 140 120 100 80 Dec-02 Dec-04 Dec-C6 Dec-08 Dec-10 Dec-12 Sant' OC4MMO Beat illocenteg Ammo LI In the following section we show results for only a select number of strategies studied. The results are largely consistent across other strategies studied and are available in the Appendix. Strategies involving selling 1M options to finance the longer-dated —ATM calls have had higher risk-adjusted returns than equity and outright calls Strategies involving selling 1M options to finance the longer-dated near-the- money calls have had slightly better performance than outright calls: these had 5 Please note that a 6% premium strategy targets trading a strike that nets a total 6% premium for the specific maturity (not annualized). Only the premium for the 1M 2% options are annualized: strikes are chosen corresponding to 2%/12 premium. 8 Please see the Appendor for an expended table of all strategies studied Deutsche Bank Securities Inc. Page 7 EFTA01077904 3 December 2013 US Derivatives Spotlight slightly higher returns at slightly lower volatility vs. outright calls. However, they did have equivalent to slightly higher volatility than some of the call spread strategies (see Figure 11 and Figure 12). Figure 11: 36M calls and spreads rolled after 24M, Dec- Figure 12: 18M calls and spreads rolled after 12M, Dec- 02 through Sep-13 02 through Sep-13 25% 25% SPX Total SPX Total Return Return • 20% • 75 36M ATM Call 36M ATM call 18M 5% cy Prem. Call e 18M ATM Call y lox • •_a Shon 1M 36M 6% Short 1M 2% ♦ V 2% Mn. 18M ATM Cal Prem. Cal Mn. Prem. Prem. Call Call 18M 5% • • Short 1M ♦ 36M 6% 36M ATM Cal s% 2% Ann. 5% - ♦ Prem. Gllt a Neill. Call . Short 38M 1 Pratt Call 18M 5% Short 18M 1% Sheet 36M 2% 2% Prem. Ca Prem. Cal Prem. Call Prem. Cal 0% 0% 0% 2% 0% 6% 8% 0% 2% a% 8% 8% AnilLialiZed Bettie, Amualized Return Sawn. DAIWA. Bate. AVOOmbtvg Avant., LP SOW*: ANOVA& Cm* AVO0mOtg Aiwa LP These results are consistent with our previous research showing that implied volatility risk premium is typically rich for short-dated options'. That is, 1M implied volatility tends to be higher than 1M realized volatility. So, selling 'expensive' 1M upside call options to finance the purchase of longer-dated calls has generally been attractive. Strategies selling 1M SPX calls have not performed recently Looking again at Figure 10 above, strategies selling 1M calls have, not surprisingly, "banked" close to the entire 2% annualized premia only during market downtums (for instance, compare the performance of ATM calls and ATM — 1M 2% calls for the Oct-07 to Mar-09 period in the table). In the rising markets of Dec-02 to Oct-07, these strategies "banked" -418% to 1.2% of the 2% premia depending on the strategy. However, the bull market between May-09 to Sep-13 saw strategies selling 1M options have lower retums than buying outright calls. This is largely due to the Apr-13 to Sep-13 period, which saw large up and down moves that resulted in large losses from some of the short 1M call that were rolled every month while the long-dated call was up relatively little (see Figure 13). 7 Please see The DNA of Ovenvnttng - A US Perspective. 02-Alx-2013. contact Page 8 Deutsche Bank Securities Inc. EFTA01077905 3 December 2013 US Derivatives Spotlight Figure 13: The Apr-13 to Sep-13 period has seen significant underperformance from financing long-dated calls with 1M calls 115% -4 E 103% 101% 99% 97% 95% Dec-02 Dec-04 Dec-06 Dec-08 Dec-10 Dec-12 Soweto: Deutsche B BloombergSeranoi LP The backtest period is very representative for 1M risk The main risk of the short 1M call occurs in violent rallies. Figure 14 shows that the frequency of sharp rallies in our backtest period is comparable to that from the prior —50 years. If anything, we tended to see slightly higher occurrences of big 1M rallies in our backtest period. 'Figure 14: Distribution of 1M SPX returns 14% 12% — Jan 195010 Nov-2002 t 10% — Dec 2002 to Sep-2013 8% O 6% 0 • 4% 2% 0% eit144#V4 4 4t?e,t:i 4 4 4 4egai441,e,tegeg4g 5 4 1M Return Bucket Sant Dame»&M. BloontOoryy Searcy IP Call spreads have had better risk-adjusted performance than all other strategies studied Spreading a call option by selling a higher strike call reduces net delta exposure. So, call spreads tend to have lower returns in rallying markets but provide better downside protection (see Figure 9 above). However, looking at the entire backtest period between Dec-02 and Sep-13 (both up and down markets), we find that call spreads tended to have annualized returns largely in line with outright call positions. Not surprisingly, call spread strategies experienced much lower volatility and higher risk- adjusted returns (see Figure 15 to Figure 18). Deutsche Bank Securities Inc. Page 9 EFTA01077906 3 December 2013 US Derivatives Spotlight Figure 15: Call spread returns similar to calls (36M calls Figure 16: ... but with much higher risk-adjusted returns and spreads rolled after 24M)... (36M calls and spreads rolled after 24M) 9% 80% 3- C 8% - 7% - 1>a 60% 70% 6% ea i.„ 50% tc 5% 1 40% 1: 4% &30% E 3% 2% 'E _t, 20% 1% 2 10% 0% 0% EquitY Outright: Spread: Spread: Outright: Spread: Equity Outright: Spread: Spread: Outright: Spread: ATM ATM - 6%ATM -2% 10% 10% - 2% ATM ATM - 8%ATM - 2% 10% 10%-2% Saint Dames Bank BlositeorgFatanoi LP sows.Dames Bank Blositeorg Arancv LP 1 Figure 17: Call spread returns similar to calls (18M calls Figure 18: ... but with much higher risk-adjusted returns and spreads rolled after 12M)... (18M calls and spreads rolled after 12M) 9% 90% Z • 80% j 70% is 60% 50% q4% 40% g3% La" 30% 2% 20% 1% 10% 0% 1.1 0% Equity Outright: Spread: Spread: Outright: Spread: Equity Outright: Spread: Spread: Outright: Spread: ATM ATM - 3%ATM -1% 5% 5% - 1% ATM ATM - 3%ATM - 1% 5% 5% - 1% Saner Deutsch, Seat avant.; 'nonce LP Sane: Ofterche Sank &combo" Amoco LP Given the attractive levels of long-dated calls currently, investors may still want to stick with outright call options rather than spreads to maintain a higher delta. However, an alternative approach could be to scale up the call spread notional and have a similar delta exposure (at least initially) to an outright call. In Figure 19 and Figure 20, we look at the risk-adjusted returns for different call and call spread strategies after we scale up the call spread notionals. We assume that the investor trades an equivalent initial delta on the call spread as an outright call, which is then only rebalanced on the roll date of the long- dated call. For instance, if on trade date the 36M ATM call option has a delta of 0.50 and the 36M ATM-6% premia call spread has a delta of 0.20, we would buy 2.5x contracts of the call spread instead of each call contract. In the historical backtests, returns and risk-adjusted returns are both better for call-spreads after scaling to equivalent delta as the outright call. The higher delta notional does increase the volatility more than the return of the call- spread strategies and drives down the return/vol slightly from what's shown in Figure 16 and Figure 18. Page 10 Deutsche Bank Securities Inc. EFTA01077907 3 December 2013 US Derivatives Spotlight Figure 19: Annualized retums/realized volatility for 36M Figure 20: Annualized retums/realized volatility for 18M calls and spreads rolled after 24M, Call spread notional calls and spreads rolled after 12M, Call spread notional scaled by delta scaled by delta 60% 70% 65% 55% 60% 50% 1 55% 45% 50% 45% 40% 40% 35% 35% 30% 30% Outright: Spread: Spread: Outright: Spread: Outright: Spread: Spread: Outright: Spread: ATM ATM - 6% ATM - 2% 10% 10% - 2% ATM ATM - 3% ATM - 1% 5% 5% - 1% Sawa 0.44701,0 an Same. Oxman eat* Roll prior to expiry Figure 21 and Figure 22 show that rolling the call spread position before expiry would have generally (but not always) resulted in higher risk-adjusted returns, across many different strategies*. Rolling prior to expiry allows you to reduce the negative effects of time decay, since shorter-dated options lose their time value quickly. Rolling early also allows you to re-strike the calls, which is especially important for options that have become far out-of-the-money. Rolling will rebalance the delta exposure higher in these cases. However, note that rolling early will result in higher transactions cost. I Figure 21: Annualized returns/realized volatility for 36M spreads 100% 90% . • Spread: ATM - 1M 2% • Spread: ATM - 6% I Figure 22: Annualized retums/realized volatility for 18M spreads 120% • Spread: ATM - 1M 2% • Spread: 9% - 3% 1 80% . Spread: 6% - 2% 100% Spread: 5% - 1% 70% - 80% 60% - 50% - 60% 40% - 30% - 40% 20% - 10% • 20% 0% 0 0% • cc cc • cc • cc • cc • cc CC ▪ 15 6 a 15 • cc cc CC • CC CC CC cc CC CC •0 • CV A 3 2 CV Sown Deveseht Bag Sweat Devesthe Ban* 8 Results for rolling prior to expiry hold for outright calls as well Deutsche Bank Securities Inc. Page 11 EFTA01077908 3 December 2013 US Derivatives Spotlight Understanding volatility, rate, and dividend yield risks for long-dated calls In this section we provide a more in-depth look at how implied vols evolve after a spot rally and also how changes in rates and dividends impact the price of calls. Vega - implied volatility sensitivity Buyers of options are long vega, and an increase in implied volatility will result in an increase in the price of a call option. Vega is proportional to time-to- maturity: longer-dated options have higher vega and as time passes the sensitivity of the options to changes in implied volatility declines. Investors holding outright long calls will benefit from the delta exposure in a SPX rally, but will likely suffer from implied volatilities decreasing in two ways: • Tenn-structure effect: As time passes, the implied volatility will slide down the typically upwards-sloping implied volatility term-structure, all else equal. • Skew effect: Implied volatility changes are negatively correlated with spot changes (see Figure 24: spot higher, implied volatility lower). Thus, as spot prices move around, the reference implied volatilities will change. However, the most recent six months have seen long-dated fixed-strike (not ATM) implied volatilities rise slightly as the market has rallied (these would correspond to points in the upper right quadrant in Figure 24), a situation that has helped these call positions doubly. In Figure 23 and Figure 24 we look at the relative magnitude of the decrease in fixed-strike implied volatilities contingent on a market rally. It is notable that the fixed-strike implied volatilities change has been on the order of 1-2 vol points in our table. Not surprisingly, longer-dated options have lower volatility sensitivity to spot price moves, and a bigger move is associated with sharper implied volatility declines. Figure 23: Median change in fixed-strike implied vol Figure 24: Regressing spot changes and changes in 36M given a minimum spot move over the period (Dec-02 to fixed strike implied vols over the subsequent 6M Sep-13) 15% Median Change in Vol After Spot Move Over Period Spot Move IBM Call After 36M Call After 60M Call After 1 10% y = -0.1299x + 0.004 (Greater Than) 6M 18M 24M 0% -0.3% -0.1% -0.2% 5% 4.8% -0.3% -0.3% 10% -1.0% -0.7% -0.5% 15% -1.4% -1.1% -0.7% 20% -2.0% -1.7% -1.0% -60% -45% -30% -15% 0% 15% 30% 45% 60% Spot Return SanDeutsch, Bert I Sane:Deutsch: Bern Page 12 Deutsche Bank Securities Inc. EFTA01077909 3 December 2013 US Derivatives Spotlight The figures below show the simulated P/Ls for 36M and 18M ATM options under different volatility and spot change scenarios after one-year has passed. The price sensitivity to spot moves does tend to dominate any volatility P/L. Also, you can see for the 36M trade that if fixed strike vols and spot are unchanged then your option loses a fifth of its value due to time decay (the 18M option loses almost half its value in the same situation). A 5% up move in spot and a 100 bps decline in vol leaves the 36M ATM call option holder relatively flat. Figure 25: Simulated P/L of 36M ATM options after 12M Figure 26: Simulated P/L of 18M ATM options after 12M have passed under different volatility and spot change have passed under different volatility and spot change scenarios (all else held the same) scenarios (all else held the same) %ChinnIn Spat %amp In Spat -10% 4% 0% 5% 10% -10% 4% 0% 5% 10% -5.00 -81% -87% .48% -22% 8% 4.00 -99% -91% -68% -23% 39% ♦.50 -79% -85% -45% -20% 11% ♦.50 -98% -90% -66% -21% 40% ♦.00 -77% -83% -42% -17% 13% ♦.00 -98% -88% -84% -20% 41% -350 -78% 40% -40% -14% 16% -3.50 -97% -87% -62% -18% 42% -3.00 -74% 68% -37% -11% 19% -3.00 -98% -85% 40% -16% 43% -2.50 -72% 45% -34% 4% 21% -2.50 -98% -84% 48% -14% 44% -2.00 -70% -53% -32% -6% 24% -2.00 -96% -82% 46% -12% 45% 450 -68% -51% -29% -3% 27% -1.50 -94% -81% -54% -10% 47% -1.00 -66% -48% -27% -1% 29% -1.00 -93% -79% 41% -8% 48% -0.50 43% -46% -24% 2% 32% -0.50 -92% -78% -49% -6% 49% 0.00 -61% -43% -21% 5% 35% 0.00 -91% -78% -47% .4% 51% 0.50 -59% -41% -19% 8% 38% 0.50 40% -74% -45% -3% 52% 1.00 47% -38% -16% 10% 40% 1.00 -89% -72% -43% -1% 54% 1.50 -56% -36% -13% 13% 43% 1.50 -88% -71% -41% 1% 56% 2.00 -53% -34% -11% 16% 46% 2.00 -87% -68% -39% 3% 57% 2.50 -50% -31% -8% 19% 48% 2.50 -88% -67% -37% 5% 59% 3.00 -48% -29% 4% 21% 51% 3.00 -84% -68% -35% 7% 60% 3.50 .46% -26% -3% 24% 54% 3.50 43% -64% -33% 9% 62% 4.00 -44% -24% 0% 27% 57% 4.00 -82% -62% -31% 11% 64% 4.50 -41% -21% 3% 29% 59% 4.50 -81% -60% -29% 13% 66% 5.00 -39% -19% 5% 32% 62% 5.00 -79% -58% -27% 15% 67% Sacak Dautsche Bane saws Atutszne Ban* Deutsche Bank Securities Inc. Page 13 EFTA01077910 3 December 2013 US Derivatives Spotlight Rho - interest rate sensitivity Interest rate levels drive the pricing of call options in two ways. • The discounting or present value effect: the present value of the expected payoff from the call at maturity is lower. • The forward effect: The cost of carry is lower and hence the expected spot is higher at maturity. This increases the value of the call. The net effect of these two can be seen by the greek 'rho', which measures the sensitivity of an option with respect to interest rates. Rho is positive for a call option, meaning that the net effect of a rise in rates will be an increase in the call price. The price increase due to the forward rising is higher than the discounting effect. Longer-dated options have higher rate sensitivity (see Figure 27). This makes sense as the forward will be affected more for longer-dated options (as the rate is scaled by the time to maturity). Thus as an option becomes closer to maturity (all else equal), its exposure to changes in interest rates falls rapidly. Because of the changing nature of the interest rate sensitivity (see Figure 28) and the relatively small impact on P/L, investors shouldn't trade long-dated calls solely to gain exposure to higher rates. However, the currently low rates (and low rates volatility) do lead to optically better relative pricing for investors wishing to be long, and any rate increase will have a positive impact on call premia (see Figure 29 and Figure 30). 'Figure 27: Call prices increase with rising rates 'Figure 28: Rho for an ATM call increases with maturity 18% 17% - 16% - 15% - 8% - 3 It 14%- 13% - 7% - z 6% - CI 12%- 5% 11% s36M ATM Call 4% ,