Options on 10-Year U.S. Treasury Note & Euro Bund Futures in Fixed Income Portfolio Analysis

Whitepaper

White Paper

Options on 10-Year U.S. Treasury Note &

Euro Bund Futures in Fixed Income

Options on 10-Year U.S. Treasury Note & Euro

Bund Futures in Fixed Income Portfolio Analysis

Contents

Introduction ... 2

Portfolio and Benchmark Example ... 3

Options Hedge Ratios and Portfolio Duration Targeting ... 5

FactSet Total Return Calculations ... 9

Attribution of Portfolio and Benchmark Returns... 10

Summary and Conclusions ... 14

Introduction

Recently, the financial markets have experienced periods of de-regulation, boom and bust, and re-regulation. Price and interest rate volatility increased and market participants learned to manage risk by developing hedging tools and techniques to safeguard their balance sheets. Financial futures and options, interest rate and currency swaps, credit default swaps, and other derivatives instruments are widely embraced in the fixed income, foreign exchange, and equity markets as risk management tools. The economic functions served by the derivative markets include trading, price discovery, and risk transfer. The financial futures, options, and swaps markets are highly liquid centralized markets that have become important trading markets. By virtue of their ease of execution, depth, and narrow bid/ask spreads, professional traders can move in and out of positions anonymously. The process of price discovery unfolds as bids and offers of quantities to be transacted are disclosed in the centralized exchanges, and this information is rapidly disseminated to the public via the reporting systems of the exchanges. These prices provide all participants, including traders, speculators, hedgers, and regulatory officials a reference to evaluate investment alternatives against and gauge market conditions. The derivative markets also facilitate the transfer of risk from individuals who want to reduce their exposure to adverse price changes to those willing to accept such exposure. The former group consists of hedgers who want to separate the normal business risk of their day-to-day activities from the risk of price or interest rate movements over which they have little or no control. The latter group consists of

Major exchanges exist in all time zones, trading a variety of dollar and non-dollar fixed income, foreign exchange, and equity derivatives. This paper focuses on options on financial futures, specifically 10-year U.S. Treasury Note and Euro Bund futures contracts and builds off the FactSet “Government Note and Bond Futures in Fixed Income Portfolio Analysis” white paper.1

Exchange-traded options on 10-Year U.S. Treasury Note and Euro Bund futures are standardized contracts that give the purchaser the right, but not the obligation, to purchase or sell the security underlying the option. As with the underlying financial futures contracts, option contracts are

standardized with respect to the quality and quantity of the deliverable grade, trading months, hours of trading, and daily price limits. Options can be purchased or sold. The buyer of a call (put) has the right to purchase (sell) the underlying futures contract. Conversely, the seller of a call (put) has the obligation to sell (buy) the underlying futures contract if the buyer exercises the option. The price at which a call or put option can be exercised is called the “strike price” or “exercise price” and the price paid for the option by the purchaser is called the “option premium.”

Portfolio and Benchmark Example

This paper explores the use of options in portfolio management, specifically for duration hedging purposes. The impact of the options is explored in terms of portfolio statistics, total return, and

performance attribution and is highlighted by an example based on a sample portfolio and benchmark. The sample portfolio includes multi-currency global bonds and is benchmarked against a multi-currency global index. The sample portfolio consists of U.S. and European government and corporate bonds denominated in GBP, EUR, and USD currencies. This sample portfolio, with and without the options, is compared repeatedly to the benchmark to demonstrate the impact of the options. The example uses a portfolio characterized by the distributions shown in Table 1:

Table 1: Portfolio Characteristics

Percent Moody's Rating Yield to Maturity OAS Effective Duration Effective Convexity Total 100.00 A2 2.95 138 5.17 0.55 GBP 11.18 A2 3.83 140 8.45 1.81 EUR 39.52 Baa2 2.95 193 4.20 0.25 USD 49.30 Aa3 2.75 93 5.20 0.51

The benchmark is defined to include GBP, EUR, and USD fixed rate securities with final maturities of one year or longer and minimum par amounts outstanding of $300 million for USD securities, €300 million for pan-European securities, and £200 million for GBP securities. The benchmark included over 12,150 securities and was characterized by the distributions in Table 2:

1

Table 2: Benchmark Characteristics Percent Moody's Rating Yield to Maturity OAS Effective Duration Effective Convexity Total 100.00 Aa3 2.33 65 5.48 0.56 GBP 8.15 Aa3 2.96 37 8.43 1.39 EUR 36.13 A1 1.93 81 5.45 0.55 USD 55.73 Aa2 2.5 59 5.06 0.44

The relative characteristics, portfolio minus benchmark, are shown in Table 3. The portfolio has a lower allocation to USD, a higher allocation to EUR, and a higher allocation to GBP when compared to the benchmark. On a weighted-average basis, the portfolio exhibits a lower overall quality rating, a higher yield to maturity, and a higher option-adjusted spread (OAS) than the benchmark. The effective duration of the portfolio is 0.31 shorter than the benchmark due primarily to the portfolio’s concentration of shorter duration EUR denominated securities.

Table 3: Relative Characteristics

Percent Moody's Rating Yield to Maturity OAS Effective Duration Effective Convexity Total 0.00 Lower 0.62 73 -0.31 -0.01 GBP 3.03 Lower 0.87 103 0.02 0.42 EUR 3.39 Lower 1.02 112 -1.25 -0.30 USD -6.43 Lower 0.25 34 0.14 0.07

In Table 3, you can infer several portfolio strategy bets from the relative exposures. First, the portfolio’s percentage allocations suggest that the GBP and EUR currency sectors are favored at the expense of USD. Second, an implicit quality bet favors lower-rated securities. Third, the relative durations suggest an expectation that EUR rates are expected to increase and USD interest rates are expected to decrease. For purposes of introducing options into the portfolio, suppose that the portfolio manager decides to remove the relative interest rate exposures in the EUR and USD sectors. In other words, the manager decides to neutralize the sector duration bets by making each portfolio sector’s duration equal to that of its respective benchmark sector. This involves extending the portfolio’s EUR sector duration from 4.20 to 5.45 and shortening the USD sector duration from 5.20 to 5.06. You could also accomplish these duration adjustments in the cash market by restructuring the bonds held in those sectors. However, trading options or futures can provide a more efficient and cost effective means to target sector durations, especially if the cash market bonds are thinly traded.

In the “Government Note and Bond Futures in Fixed Income Portfolio Analysis” white paper, we used 10-Year U.S. Treasury Note and Euro Bund futures to achieve the same sector duration goals as described above. So, why would a portfolio manager choose to use options on futures instead of the futures themselves to hedge portfolio or sector durations? The answer depends on the manager’s goals and outlook regarding the future direction of interest rates and on his willingness to pay up front for hedge protection. If the manager’s intent is to lock in a specific duration target regardless of the future direction of interest rates, futures contracts may be the better choice. If the manager desires

to pay up for that one-sided protection, options may be the better strategy. The example in this paper demonstrates the manager paying up front via the option premium for one-sided protection. The example will show how this scenario develops, particularly in the EUR sector where there is an implied expectation that Euro rates will rise.

Table 4 displays the options used in this example. Call options on Euro Bund futures and put options on 10-year U.S. Treasury Note futures contracts are used to hedge the interest rate exposure in the EUR and USD sectors respectively. Both options are slightly out of the money, meaning that the strike price of the call option (139.5) is above the price of the underlying Euro Bund futures contract (139.17) and the strike of the put option (122.5) is below the price of the underlying 10-year U.S. Treasury Note futures contract (123.05).

Table 4: Options on Euro-Bund and U.S. 10-Year Treasury Note Futures

Exchange FactSet Ticker Option Type Strike Price Underlying & Contract Value Delivery Months Call Option on Euro-Bund Futures Eurex RXH4C139.5 Call 139.5 Euro-Bund Future €100,000 Nearest 3 calendar months and following 4 months in the Mar, Jun, Sep, Dec quarterly cycle

Put Option on U.S. 10-Year Treasury Note Futures

CME TYH4P122.5 Put 122.5

10-Year Treasury Note Future $100,000

At least 4 consecutive contract months plus the next 4 months in the Mar, Jun, Sep, Dec quarterly cycle

Both of the options specify the physical delivery of one futures contract. The notional of the futures contracts is €100,000 for the Euro Bund contract and $100,000 for the 10-year U.S. Treasury Note contract.

FactSet calculates interest rate sensitivities for options contracts, including partial and effective

durations and convexities. The internal calculation initially solves for the implied volatility that produces the market value. The reference yield curve is shifted up and down by 100 basis points, and the price of the option is recalculated by holding the implied volatility constant. The difference in the up and down prices due to the yield shift result in the partial and effective durations. Based on these calculations, FactSet calculates options durations and partial durations daily and you can use these to construct hedge ratios for purposes of targeting portfolio or sector durations.

Options Hedge Ratios and Portfolio Duration Targeting

𝑁 =(𝐷𝑇− 𝐷𝑃) ∗ (𝑀𝑉 + 𝐴𝐼)𝑃 𝐷𝑂∗ (𝑀𝑉)𝑂

where:

+ 𝑁 = Number of options contracts

+ 𝐷_𝑇 = Target duration of the hedged portfolio (or sector) + 𝐷_𝑃= Duration of the unhedged portfolio (or sector)

+ (𝑀𝑉 + 𝐴𝐼)𝑃= Market value and accrued interest of the portfolio (or sector) + 𝐷_𝑂 = Duration of the options contract

+ (𝑀𝑉)𝑂 = Notional market value of the options contract

Returning to the portfolio/benchmark example, you can use the formula above to target a EUR sector duration of 5.45 as follows:

𝑁 =

(5.45 − 4.20) ∗ €66,540,361

508 ∗ €976

= 168

The market value and accrued interest of the EUR sector of the portfolio is €66,540,361, the duration of the call option is 508, and the market value per call option contract is €976 (see Table 5 for options data). A long position of 168 call options with a strike price of 139.5 on the March ’14 Euro-Bund futures contracts increases the effective duration of the EUR sector from 4.20 to 5.45, thereby eliminating the duration difference between the portfolio and benchmark.

You can use a similar calculation to compute the required number of put options to reduce the effective duration of the USD sector from 5.20 to 5.06. In this case, 47 put options with a strike price of 122.5 on the March ’14 10-Year Treasury note futures are purchased to make the duration of the USD sector in the portfolio equal to the respective sector in the benchmark.

In FactSet, all options and futures positions are displayed in terms of their equivalent notional

Table 5: Options Statistics, Durations, and Convexities

Mar '14 139.5 Call on Bund Futures

Mar '14 122.5 Put on 10-Year U.S. Treasury Note Futures FactSet Symbol RXH4C139.5 TYH4P122.5

Ending Price (Local) 0.97641 0.65234*

Ending # of Contracts 168 47

Ending Notional Exposure 16,800,000 4,700,000

Ending Market Value € 164,037 € 22,250

Ending Weight 0.10 0.01

Ending Options Delta 0.46 -0.40

Ending Partial Durations

2-Year 3.43 0.75

5-Year 74.69 -330.28

10-Year 429.83 -193.66

30-Year -- --

Ending Effective Duration 507.95 -523.19

Ending Effective Convexity 2002 1581 * Exchange quoted price converted to 64ths for Options on U.S. Treasury Futures

Table 5 shows the option notional amounts required to neutralize the EUR and USD sector durations relative to the benchmark. The portfolio is long €16,800,000 notional of call options on Euro-Bund futures, equivalent to 168 contracts. The portfolio is long $4,700,000 notional of put options on 10-year U.S. Treasury Note futures, equivalent to 47 contracts.

The partial durations, effective duration, and effective convexity for each options position is also shown. For instance, the call option on Euro-Bund futures has an effective duration of 508 (rounded) and the put option on 10-Year U.S. Treasury Note futures has an effective duration of -523. The duration of the put option is negative because the long put option is equivalent to being short the underlying 10-year U.S. Treasury Note futures contract upon exercise, which would have a negative effect on portfolio duration. Conceptually, you can think of the effective durations and convexities of the options contracts as the product of the duration and convexity of the underlying deliverable (i.e., futures contract), the option delta, and a ratio of the underlying price to the options price. That ratio reflects the leverage created by a position in the options. The higher the price of the underlying instruments relative to the price of the options, the greater the leverage. High leverage results in large durations and convexities and increased interest rate exposure per dollar of investment.

The contribution to effective duration and contribution to convexity of the options are calculated as the product of the market value percent and the duration/convexity statistics. Generically, you can

calculate the contribution to effective duration as:

You can calculate contribution to effective duration at the portfolio level or at the sector level. At the portfolio level, the calculation uses the portfolio weight and at the sector level, it uses the sector weight. For instance, the contribution to duration of the call options on Euro Bund futures to the duration of the EUR sector is equal to 1.25 ((€164,037 / €66,540,361) * 508). The weight is calculated as the market value of the options position divided by the market value of the EUR sector. The call options contribute 1.25 to the duration of the EUR sector, increasing it from 4.20 to the EUR benchmark duration of 5.45. The effect of the Euro-Bund call options strategy is to neutralize the EUR sector’s relative interest rate sensitivity to changes in EUR rates.

You can perform a similar calculation for the put options. In this case, a long position of 47 contracts contributes -0.14 ((€22,250 / €83,034,528) * -523) to the portfolio’s USD sector duration, reducing it from 5.20 to 5.06. Again, the put strategy eliminates the relative exposure to changes in USD interest rates.

At the portfolio level, the impacts of the options strategies are illustrated in Table 6 and Table 7. Table 6 displays the portfolio results excluding the options and Table 7 shows similar results including them:

Table 6: Portfolio, Excluding Options, versus Benchmark

Variation Market Value Percent Portfolio Ending Effective Duration Benchmark Ending Effective Duration Portfolio Ending Effective Convexity Benchmark Ending Effective Convexity Variation Ending Duration Variation Ending Convexity Total 0.00 5.17 5.48 0.55 0.56 -0.31 -0.01 GBP 3.03 8.45 8.43 1.81 1.39 0.02 0.42 EUR 3.39 4.20 5.45 0.25 0.55 -1.25 -0.30 USD -6.43 5.20 5.06 0.51 0.44 0.14 0.07

In Table 6, notice the discrepancy in the ending effective durations of the EUR and USD sectors, -1.25 and 0.14 respectively. In the example, the call options on Euro-Bund futures and the put options on 10-year U.S. Treasury Note futures are included in the portfolio specifically to neutralize these

discrepancies. The results of including those options are shown in Table 7:

Table 7: Portfolio, Including Options, versus Benchmark

the GBP and EUR sectors and the effective durations of those sectors are longer than the effective duration of the USD sector, which is underweighted.

By including options positions, which are highly leveraged, it also increased the overall convexity of the portfolio relative to benchmark, from -0.01 to 2.15.

FactSet Total Return Calculations

Options on Treasury Note and Bund futures generate no coupon or principal cash flows, and therefore, consist entirely of price return.

In FactSet, price return is always displayed in local currency terms. In a multi-currency portfolio, total return is reported in a user-selected reporting currency and includes a currency return component:

𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑡𝑢𝑟𝑛 = 𝑃𝑟𝑖𝑐𝑒 𝑅𝑒𝑡𝑢𝑟𝑛 + 𝐶𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑅𝑒𝑡𝑢𝑟𝑛

Currency return is calculated as:

𝐶𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑅𝑒𝑡𝑢𝑟𝑛 = 𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑡𝑢𝑟𝑛 (𝑟𝑒𝑝𝑜𝑟𝑡 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦) − 𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑡𝑢𝑟𝑛 (𝑙𝑜𝑐𝑎𝑙 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦)

To calculate total return in a reporting currency that is different than the local currency, FactSet applies exchange rate adjustments to the local price return as follows:

𝐶𝑢𝑟𝑟𝑒𝑛𝑐𝑦– 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑡𝑢𝑟𝑛 =

(𝑃

− 𝑃

)

(𝑃

+ 𝐴𝐼

)

∗ (

𝐹𝑋

𝐹𝑋

)

+ 𝐴𝐼_𝑏= Beginning Accrued Interest + 𝐹𝑋_𝑒= Ending FX rate

+ 𝐹𝑋_𝑏 = Beginning FX rate

Table 8: Total Return Components and Contributions – Portfolio, Excluding Options, versus Benchmark

Return Components Total Returns & Contributions Variation

Port. Price Return (Local) Port. Coupon Return (Local) Port. Currency Return Port. Total Return (EUR) Port Contribution to Return (EUR) Bench. Total Return (EUR) Bench Contribution to Return (EUR) Total Return (EUR) Total 1.42 0.31 1.25 2.97 2.97 2.98 2.98 -0.01 GBP 1.43 0.48 1.42 3.32 0.35 3.51 0.29 -0.19 EUR 1.83 0.33 0.00 2.16 0.87 1.84 0.66 0.32 USD 1.08 0.26 2.21 3.55 1.75 3.64 2.03 -0.09 The Return Components section of Table 8 shows portfolio price return, portfolio coupon return, and portfolio currency return. The Total Returns & Contributions section shows total returns for the portfolio and benchmark, as well as the contributions to total returns by currency sector. Finally, the Variation section shows the difference in total return between the portfolio and the benchmark. For the period, the portfolio total return was one basis point less than the benchmark total return. Positive relative contributions in the EUR and GBP sectors (0.21 and 0.06, respectively) were more than offset by negative contribution from the USD sector (-0.28). Table 9 shows similar data for the portfolio, including the options:

Table 9: Total Return Components and Contributions – Portfolio, Including Options, versus Benchmark

Return Components Total Returns & Contributions Variation Port. Price Return (Local) Port. Coupon Return (Local) Port. Currency Return (Local) Port. Total Return (EUR) Port Contribution to Return (EUR) Bench. Total Return (EUR) Bench Contribution to Return (EUR) Total Return (EUR) Total 1.74 0.31 1.25 3.30 3.30 2.98 2.98 0.32 GBP 1.43 0.48 1.42 3.32 0.35 3.51 0.29 -0.19 EUR 2.66 0.33 0.00 2.99 1.20 1.84 0.66 1.15 USD 1.05 0.26 2.21 3.52 1.74 3.64 2.03 -0.12 The portfolio’s total return for the holding period was 3.30%, up from 2.97% shown in Table 8. The total return of the portfolio relative to the benchmark also increased by the same amount. The options added to portfolio total return, but how? To answer this question, we turn to benchmark-relative performance attribution.

Attribution of Portfolio and Benchmark Returns

Table 10: FactSet Basic Performance Attribution Model

Portfolio

Strategy Strategy Variable Attribution Factor (Effect) Interest rates Effective Duration Shift

Yield Curve Partial Durations Twist

Sector Allocation Sector weight (%) Allocation

Bond Selection Bond Weight (%) Selection

Currency Currency weight (%) Currency

The attribution factors include shift, twist, allocation, selection, and currency. For a full explanation of FactSet’s attribution methodology, reporting configurations, and calculation details, see “A Flexible Benchmark Relative Method of Attributing Returns for Fixed Income Portfolios.” 2 One advantage of FactSet’s approach is that a common methodology and set of calculations are used for all security types, including options on government note and bond futures.

For interest rate related options, the most relevant attribution factors are shift and twist since options on futures are primarily interest rate sensitive instruments.

Shift return is calculated as:

𝑆ℎ𝑖𝑓𝑡 𝑅𝑒𝑡𝑢𝑟𝑛 = −1 ∗ 𝐸_{𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛}∗ Δ_{𝑆ℎ𝑖𝑓𝑡 𝑃𝑜𝑖𝑛𝑡+ 1 2}⁄ ∗ 𝐸_{𝐶𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦}∗ (Δ𝑆ℎ𝑖𝑓𝑡𝑃𝑜𝑖𝑛𝑡)2

Twist return is calculated as:

𝑇𝑤𝑖𝑠𝑡 𝑅𝑒𝑡𝑢𝑟𝑛 = (−1 ∗ 𝐸_{𝑃𝑎𝑟𝑡𝑖𝑎𝑙𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛1}∗ (Δ𝑃𝑎𝑟𝑡𝑖𝑎𝑙𝑃𝑜𝑖𝑛𝑡1− Δ𝑆ℎ𝑖𝑓𝑡𝑃𝑜𝑖𝑛𝑡)) + (−1 ∗ 𝐸𝑃𝑎𝑟𝑡𝑖𝑎𝑙𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛2∗ (Δ𝑃𝑎𝑟𝑡𝑖𝑎𝑙𝑃𝑜𝑖𝑛𝑡2− Δ𝑆ℎ𝑖𝑓𝑡𝑃𝑜𝑖𝑛𝑡)) + (−1 ∗ 𝐸_{𝑃𝑎𝑟𝑡𝑖𝑎𝑙𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛3}∗ (Δ𝑃𝑎𝑟𝑡𝑖𝑎𝑙𝑃𝑜𝑖𝑛𝑡3− Δ𝑆ℎ𝑖𝑓𝑡𝑃𝑜𝑖𝑛𝑡)) … + (−1 ∗ 𝐸_{𝑃𝑎𝑟𝑡𝑖𝑎𝑙𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛𝑁}∗ (Δ𝑃𝑎𝑟𝑡𝑖𝑎𝑙𝑃𝑜𝑖𝑛𝑡𝑁− Δ𝑆ℎ𝑖𝑓𝑡𝑃𝑜𝑖𝑛𝑡)) 2

where:

+ E_Duration= Effective Duration

+ Δ_ShiftPoint= Change in the Yield of a UserDefined Yield Curve Shift Point + E_Convexity= Effective Convexity

+ E_{PartialDuration#}= Effective Partial Duration at a Specific Yield Curve Point + ΔPartialPoint#= Change in the Yield of a Specific Yield Curve Point

Shift and twist returns represent the portion of total return explained by changes in the level of interest rates and changes in the shape of the yield curve, respectively. Shift and twist returns exclude spread and carry components and are calculated independently of the benchmark. Subtracting shift and twist return from total return results in Residual Return:

𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑅𝑒𝑡𝑢𝑟𝑛 = 𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑡𝑢𝑟𝑛 − (𝑆ℎ𝑖𝑓𝑡 𝑅𝑒𝑡𝑢𝑟𝑛 + 𝑇𝑤𝑖𝑠𝑡 𝑅𝑒𝑡𝑢𝑟𝑛)

Residual return represents the portion of total return unexplained by shift and twist. It includes return components such as spread, income, paydown, carry (accretion and roll down), volatility, inflation, and basis.3 For options on government bond futures, residual return is primarily basis and carry.

Residual returns are used to quantify allocation and selection effects, both of which are calculated relative to the benchmark, as follows:

𝐴𝑙𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 𝑅𝑒𝑡𝑢𝑟𝑛 = ∑[(𝑊𝑖− 𝑊𝑖) ∗ (𝑅𝑅𝑖− 𝑅𝑅)] 𝑖

𝑆𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑅𝑒𝑡𝑢𝑟𝑛 = ∑[𝑊𝑖∗ (𝑅𝑅𝑖− 𝑅𝑅𝑖)] 𝑖

where:

+ W_i= Weight of Group i in Portfolio + W_i= Weight of Group i in Benchmark

+ RRi= Residual Return of Group i in Benchmark + RR = Overall Benchmark Residual Return + RR_𝑖 = Residual Return of Group i in Portfolio

Returning to the portfolio example, Table 11 shows performance attribution for the portfolio, excluding options, relative to the benchmark. The portfolio and benchmark returns are shown in both local and EUR currency terms and the attribution results are in local terms.

3

Table 11: Basic Attribution of Portfolio, Excluding Options, versus Benchmark

Local Returns EUR Returns Attribution

Port. Total Return (Local) Bench. Total Return (Local) Variation in Total Return (Local) Port. Total Return Bench. Total Return Shift Effect (Local) Twist Effect (Local) Allocation Effect (Local) Selection Effect (Local) Total Effect (Local) Total Currency Effect Total Effect Total 1.72 1.63 0.09 2.97 2.98 -0.11 0.04 0.01 0.15 0.09 -0.10 -0.01 GBP 1.90 2.09 -0.19 3.32 3.51 0.03 -0.01 0.00 0.01 0.03 0.00 0.03 EUR 2.12 1.84 0.28 2.16 1.84 -0.08 0.05 0.00 0.20 0.17 -0.05 0.12 USD 1.35 1.43 -0.08 3.55 3.64 -0.06 0.00 0.00 -0.07 -0.13 -0.05 -0.18

Over the holding period the portfolio total return in EUR was 2.97 percent ─ about one basis point less than the total return of the benchmark. The attribution results indicate that the shift (-0.11), twist (0.04), allocation (0.01), selection (0.15), and currency effects (-0.10) were largely offsetting in the aggregate.

As described previously, the Euro-Bund futures call options were purchased to lengthen the EUR sector duration by 1.25 and the 10-year U.S. Treasury Note futures put options were purchased to shorten USD sector duration by 0.14. For purposes of the example, the options positions that were determined by the hedge ratio calculation described earlier were held static during the holding period; there was no re-balancing of the derivatives as might occur in practice. During the holding period, 5-Year German government benchmark rates, a proxy for EUR interest rates, declined by about 14 basis points and 5-Year U.S. Treasury interest rates declined by about 5 basis points. Table 12 shows the total return and performance attribution results when options are included in the portfolio:

Table 12: Basic Attribution of Portfolio, Including Options, versus Benchmark

Local Returns EUR Returns Attribution

Port. Total Return (Local) Bench. Total Return (Local) Variation in Total Return (Local) Port. Total Return Bench. Total Return Shift Effect (Local) Twist Effect (Local) Allocation Effect (Local) Selection Effect (Local) Total Effect (Local) Total Currency Effect Total Effect Total 2.05 1.63 0.42 3.30 2.98 0.21 0.01 0.01 0.18 0.41 -0.10 0.31 GBP 1.90 2.09 -0.19 3.32 3.51 0.03 -0.01 0.00 0.01 0.03 0.00 0.03 EUR 2.98 1.84 1.14 2.99 1.84 0.24 0.02 0.00 0.25 0.12 -0.05 0.46 USD 1.33 1.43 -0.10 3.52 3.64 -0.06 0.00 0.00 -0.07 -0.13 -0.05 -0.18

By comparing Table 12 (including options) to Table 11 (excluding options), the impact of the derivative strategy is evident. Portfolio total return versus benchmark increased by 32 basis points (0.31 ─ -0.01). For the portfolio alone, the call options on Euro-Bund futures added 86 basis points (2.98 – 2.12) to the local return of the EUR sector, while the put options on 10-year U.S. Treasury Note futures subtracted 2 basis points (1.33 – 1.35) in local return from the USD sector. At aggregate level, the net result was an increase in total portfolio return by 33 basis points (3.30 – 2.97). The attribution reveals why.

points (0.21 – -0.11). The options strategy paid off more than expected; the aggregate level shift effect of 0.21 percent was greater than what one would expect under duration neutrality. Two possible explanations account for this. First, the options positions were held static during the holding period. As rates declined, futures prices increased and the call options went deep into the money, contributing increasing duration to the EUR sector and to the overall portfolio. At the same time, the put options went deep out of the money, becoming essentially worthless. Another way to view this is in terms of convexity and the corresponding impact it has on duration as interest rates change. Contribution to duration was impacted by convexity and the changing market value of the options, which increased for the calls and declined for the puts. In total, the call options had greater impact with regard to duration, which is why the shift effect increased as EUR interest rates declined. The large impact on portfolio convexity of options is one characteristic of this strategy that is not shared by futures strategies. This should be taken into account, along with the asymmetric return profile of options, when deciding whether to use options or futures to target sector and/or portfolio durations.

Further analysis of Table 11 and Table 12 reveals that the impact of the options on twist effects at the portfolio and sector levels was much smaller than their impact on the shift effects because both the EUR and USD yield curves generally moved in parallel over the measurement period. The allocation effect did not change at the portfolio or sector levels because the options positions had negligible impact on the portfolio sector weights. This emphasizes the high leverage characteristic of options strategies. The selection effect of the EUR sector increased modestly as a result of the call options. They had higher residual returns for the holding period compared to the corresponding index sector’s residual return, but modest low weights.

In summary, the attribution indicates a significant shift effect impact on relative performance as a result of declining EUR and USD rates when options are included in the portfolio. This is a result of the

convexity characteristics of options, and would not have occurred had futures been used instead. Also, if the options positions had been dynamically re-balanced throughout the holding period to maintain the desired sector duration targets, the shift effect would have been lower and more in line with a duration neutral strategy.

Summary and Conclusions

Options on government note and bond futures are often used by portfolio managers to hedge durations and alter interest rate exposures of global bond portfolios. The analytics and returns calculated by FactSet constitute the basis for calculating performance attribution for portfolios that include options versus benchmarks.