Do Returns on Synthetic Portfolios Constructed from Stock Index Futures Deliver Capital Gains, Dividends and Franking Credits?

Alex Frino, Grant Wearin & Joel Fabre

By Alex Frino, Grant Wearin & Joel Fabre*

Abstract Previous papers documenting the relationship between returns on stock index futures and stock indices typically ignore dividends1. This appears to leave open the issue of whether the return on a synthetic position constructed using stock index futures and a risk free asset efﬁ ciently delivers the value of dividends. This paper proves mathematically that the returns on synthetic positions using such contracts should deliver capital gains, cash dividends and the value of franking credits derived by arbitrageurs. Empirical evidence consistent with this proposition is provided, using a sample of data for the SPI 200 contract trading on the Sydney Futures Exchange. Interestingly, the evidence suggests that franking credits are priced into stock index futures contracts, despite the introduction of the 45-day rule which seemingly would appear to prevent this. JEL Classiﬁ cation: G11; G12; G13; G28 Keywords: Synthetic portfolios, stock index futures, dividends, franking credits

1. Introduction constructed using stock index futures and a fi xed income security deliver capital gains, dividends and franking credits. It With the proliferation of managed funds in the last is proven mathematically that if franking credits are priced into three decades, stock indices continue to play a central role a stock index futures contract by arbitrageurs, then returns on in benchmarking the performance of equity fund managers. synthetic positions constructed using a fi xed income security This is especially the case for index managers, who face and stock index futures deliver capital gains, cash dividends the fundamental challenge of minimizing tracking error - and the value of franking credits derived by arbitrageurs. the absolute difference between the fund return and the Empirical evidence consistent with this proposition is also index return - while controlling transaction costs2. This provided, using a sample of data for the SPI 200 contract has contributed to the development of fi nancial instruments trading on the Sydney Futures Exchange (SFE). The analysis such as stock index futures, which enable investors to obtain demonstrates that a synthetic position constructed using the SPI index exposure synthetically, that is, without physically trading 200 and a Bank Accepted Bill (BAB) outperforms the return stocks3. Compared to alternatives such as exchange-traded- on the S&P/ASX 200 Accumulation Index. Furthermore there funds or index options, index futures offer the lowest cost is a signifi cant positive relationship between outperformance method of investing in stock indices4. However, a common and franking credits paid out by the index. Interestingly, one misconception is that use of these contracts necessitates the of the implications of this empirical evidence is that franking sacrifi ce of stock dividends5. We provide a mathematical credits are priced into stock index futures contracts, despite the proof supporting the notion that a synthetic position made introduction of the 45-day rule which seemingly would appear up of stock index futures contracts and a risk free asset to prevent this. can synthetically generate the return obtained by investing in each stock in the index portfolio. Prior academic literature The remainder of this paper is organized as follows. documenting the relationship between returns on stock index Section 2 proves mathematically that the returns to synthetic futures and stock indices, focusing on hedging effectiveness, positions using stock index futures and a fi xed income typically ignores dividends6. All of these studies examine security deliver capital gains, dividends and franking credits. price indices, which omit dividends. This appears to leave Section 3 describes the data used in the empirical analysis. open the issue of whether the return on a synthetic position Section 4 provides empirical analysis of the performance and constructed using stock index futures and a risk free asset effectiveness of the synthetic position in delivering the value effectively delivers the value of dividends. This is doubly of dividends and franking credits. Section 5 concludes. important in jurisdictions such as Australia where franking credits are attached to dividends, and raises the question of whether synthetic positions also deliver franking credits. These 2. Do Stock Index Futures Deliver Dividends And Franking issues are particularly relevant to fund managers, who are Credits? typically benchmarked to accumulation indices, which include A fundamental choice for index managers is whether to dividends. replicate index returns directly by purchasing the underlying This paper provides new evidence on the relationship stocks, or synthetically through the use of instruments such between returns on stock index futures and stock indices as index futures. To replicate the return on an index, an by examining whether the returns to synthetic positions investor needs to generate the return that would be achieved

8 Journal of Law and Financial Mangement - Volume 3, No. 1 Returns on Synthetic Portfolios by holding the stocks in the index portfolio, with the correct are re-invested is precisely the same as the return on an weightings. Before taxes and transaction costs, this return accumulation index. In notational format: comprises capital gains, dividends and any franking credits T attached to the dividends. Therefore, delivery of the value of I Id TT1 ¦ t dividends and any attached franking credits contributes to the tT 1 efﬁ cacy of a replication strategy. Because index futures are rp , IT 1 normally based on price indices, there may be a perception that where: (1) returns obtained from replication strategies using index futures do not deliver the value of dividends or franking credits.

However, when combining index futures with a risk free asset IT is the value of the index portfolio at time T to create a synthetic position the returns will accrue dividends. dt is the dividend paid out by the index portfolio over The proof below demonstrates that the returns to a synthetic period t (i.e., from T-1 to T). position comprising a long position in an index futures contract and a ﬁ xed income security, in fact, replicate the return to an Synthetic Position Return accumulation index. The return on a synthetic position is given by the return There are several assumptions underlying the proof. First, on the futures contract plus the return on the bond from T-1 the proof relies on the linear cost-of-carry model to value the to T. Since the investment in the futures contract is costless, futures contract, which implies an assumption that the futures then the cost of the portfolio is simply the value of the index trade at fair value. Second, it is assumed that the interest rate portfolio (IT-1) which represents the amount of cash available representing the ﬁ nancing cost in the cost-of-carry model is for investment in the bond. Denoting the price of the futures approximately equal to the rate of return on the bond. To contract at time T as fT, then the return on the synthetic position the extent that either of these assumptions do not hold, there r’p is given by the following expression: will be some tracking error between the returns of the index T portfolio and the synthetic position. Third, for each exposition f fr TT1 ¦ t we ignore the re-investment of dividend returns that accrue to r ' tT 1 , the synthetic position7. p I where: T 1 (2) Index Portfolio Return T From one point in time T-1 to another T, the return rt on all stocks comprising the index portfolio when dividends ¦ t T 1 is the return on the bond in dollars from T-1 to T.

$1.10

$1.05

$1.00

$0.95 Value

$0.90

$0.85

$0.80

1 2 3 3 0 01 01 02 -0 -02 -02 -02 02 02 02 03 -0 -0 03 -03 03 v-01 n-02 - y c- n-03 - y a ar un Jul a ar Jul Sep- Oct- No Dec- J Feb-02 M Apr Ma J Aug- Sep-02 Oct- Nov-02 De J Feb-03 M Apr Ma Jun- Aug- Sep-03 Date

S&P/ASX 200 S&P/ASX 200 Accum Synthetic Position

Figure 1 Performance of synthetic position and accumulation index This figure shows the value of one dollar invested in the synthetic position and the accumulation index on September 1, 2001. Month-end values are reported from September 2001 to September 2003. Values are calculated month-on-month using the log returns of each position. The return to the synthetic position is the sum of the return to a long position in the SPI 200 futures contract plus the 90- day BAB yield. A rollover date of T-10 is used for the futures component of the synthetic position. The BAB yield from ten days prior to the futures expiry date is used, and is updated on rollover.

June 2004 9 Alex Frino, Grant Wearin & Joel Fabre

Average Excess Return % Positive Excess Returns Rollover Date All Months Non-Expiration Expiration Non- Expiration Expiration t-1 -0.03% 0.081% -0.213% 56% 33% t-5 -0.03% 0.081% -0.234% 56% 22% t-10 -0.02% 0.081% -0.206% 56% 11% t-15 -0.03% 0.121% -0.285% 56% 11% t-20 -0.03% 0.127% -0.307% 63% 11%

Table 1 Performance of a synthetic position relative to the accumulation index This table reports the monthly performance of a synthetic position comprising a SPI 200 futures contract and 90-day BAB over the period September 1, 2001 to September 30, 2003. Performance is assessed using monthly excess returns equal to the return on the synthetic position less the return on the S&P/ASX 200 accumulation index. Performance measures are reported for a number of rollover dates.

Index Portfolio and Synthetic Position Equivalence Since (5) is identical to (1), we have proven that the To prove that the return on the synthetic position given by return on the synthetic position is equal to the return on the (2) is equivalent to the return on the index portfolio including index portfolio plus dividends. If dt is deﬁ ned as the value dividends (1) we begin by stating the cost-of-carry model of dividends including franking credits, then trivially from (5), it follows that the synthetic position will return the value of which implies that the futures price fT can be written as follows: franking credits as well as dividends.

nn 3. Data And Method f Ird, TT ¦¦ t t The empirical analysis focuses on a widely used Australian where: tT tT (3) benchmark index, the S&P/ASX 200. Data on the cash index, associated dividends and franking credits, SPI 200 index d is the dividend paid (in dollars) by the index portfolio in t futures and returns on BABs were gathered for the period period t September 1, 2001 to September 30, 20038. Closing prices rt is the opportunity or ﬁ nancing cost of investing in the for the accumulation and price indices were downloaded from index portfolio the S&P website. The index ﬁ le contains closing index values, which are calculated and disseminated by S&P at 4:05 p.m. on n is the maturity date of the futures contract. each trading day. S&P calculates closing index values using

Using (3) the futures price fT-1 can be written as follows: the closing prices of constituent stocks, determined in the nn SEATS call auction for each stock at approximately 4:05 p.m. f Ird. TT11 ¦¦ t t Transaction data for SPI 200 futures were provided by tT 11 tT . (4) the SFE. The SFE fi le describes the prices of trades for the contract nearest to expiry and the next nearest contract, Substituting (3) and (4) into (2) yields: and is time-stamped to the nearest second. The last price ªºªºnn n n T transacted before 4:05 p.m. were extracted from the SFE I rdI r d r «»«»Tt¦¦ tT 1 ¦ t ¦ t ¦ t fi les. Only prices recorded at 4:05 p.m. were used as these ' ¬¼¬¼tT tT tT 11 tT T 1 r , are synchronized with ASX closing prices upon which the p I T 1 underlying index is calculated. The 25-minute difference in closing times would result in error in the measurement of which can be re-arranged and simplifi ed as follows: tracking error if reported futures closing prices were used9. nnn n T I Irrddr Data on 90-day BABs were gathered from a fi le containing a TT1 ¦¦¦ t t t ¦ t ¦ t ' tT tT 111 tT tT T daily time-series of BAB yields, provided by the Reserve Bank rp IT 1 of Australia. A daily time-series of accumulation and price index returns, SPI 200 returns and 90-day BAB yields was constructed TT T by joining the fi les described above. The limited life of futures I Irdr TT1 ¦¦ t t ¦ t contracts requires ‘rolling over’ to the next contract as the ' tT 11 tT tT 1 rp near contract expires in order to create a long-term series of IT 1 futures returns. Prior research has shown that rolling over at the expiry date induces spurious volatility and autocorrelation in futures returns10. As a robustness check against ‘expiry T effects’, separate futures return series were constructed from I Id price series rolled over at 1, 5, 10, 15 and 20 days before TT1 ¦ t r ' tT 1 . expiry. A month-end fi le containing the accumulation and p price index (log) returns, fi ve futures series (log) returns and IT 1 (5) one BAB yield was then constructed by summing daily data

10 Journal of Law and Financial Mangement - Volume 3, No. 1 Returns on Synthetic Portfolios within each calendar month11. The fi nal sample consists of a the 90-day BAB yield. Over the sample period, the synthetic time-series of 25 months of data. position outperforms the price index strongly (which ignores dividends), and tracks the accumulation index closely, although The return on the synthetic position is calculated by there is evidence that it slightly underperforms. Prima facie, assuming the value of the index portfolio is invested in the it appears that the synthetic portfolio returns the bulk of the fi xed income security. This represents the same amount of dividend yield paid out by the index portfolio. A rollover date funds that would be allocated among component stocks of the of T-10 for the futures is used12. It is possible that transaction index portfolio had the investment taken place in the physical costs associated with rollover of the futures component of the market. At this point one long SPI200 futures contract is synthetic position in expiration months are adversely affecting bought. The investment in the fi xed income security and the the performance of the synthetic position13. Hence the stock index futures contract combine to create the synthetic sample is partitioned into expiration months (i.e., March, June, position. Mathematically the return on the synthetic portfolio September and December) and non-expiration months. is: Excess returns equal to the difference between the 90 synthetic position return and the accumulation index return are rt u u I 0 ( fT f 0 ) u 25 ' 365 calculated to analyse the relative performance of the synthetic rp position. A positive excess return indicates that the synthetic Where: I 0 position has outperformed the accumulation index, while negative excess returns indicate underperformance. Table 1 r’p is the return to the synthetic position reports the average excess returns over the sample period r is the annual return on the risk free fi xed income t for expiration and non-expiration months, separately and security combined. Also reported are the proportion of months with a positive excess return, broken down by expiration and non- I0 is the price index at time 0 in dollars expiration months. Separate results are reported for each (f - f ) x 25 is the dollar gain / loss on the futures T 0 rollover date. (see Figure 1) component of the synthetic position assuming the futures position is rolled at time T, approximately 90 days from The results reported in Table 1 reveal substantial time 0. differences in performance between the synthetic position and the accumulation index. When all months are combined, the 4. Empirical Analysis synthetic position slightly underperforms the accumulation Relative performance of synthetic position index. Average excess returns in expiration months range from underperformance of 20.6 basis points to 30.7 basis Figure 1 illustrates the value of one dollar invested in the points, depending on the rollover date used. Substantial synthetic position and the accumulation index on September underperformance in expiration months is likely due to the 1, 2001. The return to the synthetic position is the sum of the transaction costs incurred in rolling over the futures component return to a long position in the SPI 200 futures contract plus

Coefficients Accum. Index Franking Expiration Rollover Date R Squared Return Credit Yield Dummy t-1 1.0 (56.6)* 0.4 (0.9) -0.33 (-2.3)* 99.4% t-5 1.0 (59.7)* 0.4 (1.1)* -0.35 (-2.6)* 99.5% t-10 1.0 (59.3)* 0.4 (0.9) -0.31 (-2.2)* 99.4% t-15 1.0 (59.4)* 0.7 (1.6)* -0.46 (-3.3)* 99.4% t-20 1.0 (60.4)* 1.0 (2.3)* -0.56 (-4.1)* 99.5% * indicates statistical significance at the 0.1% level.

Table 2 Regression analysis of synthetic position This table reports results from a multiple regression analysis of a monthly returns to a synthetic position comprising a SPI 200 futures contract and 90-day BAB over the period September 1, 2001 to September 30, 2003. In order to test this proposition, the following regression model was estimated: rbrbfbEe pt,1,2 AIt t 3 t t

Variable deﬁ nitions are as follows: rp,t is the return to the synthetic position in month t, rAI,t is the monthly return to the accumulation index in month t, ft is an estimate of the franking credit yield on the accumulation index in month t, Et and is a dummy variable equal to 1 if month t is an expiry month, otherwise 0. The franking credit yield was estimated by taking the difference between the accumulation index return and the price index return to obtain the dividend yield, which was then grossed-up, assuming a corporate tax rate of 30% and that all dividends in the index portfolio were fully franked. Regressions were estimated for a number of rollover dates.

June 2004 11 Alex Frino, Grant Wearin & Joel Fabre of the synthetic position around expiry. However in non- yield is positive and signifi cant. The result implies that the expiration months, average excess returns vary from +8.1 basis synthetic position also delivers outperformance which is related points to +12.7 basis points - hence the synthetic position to the value of franking credits paid out by the index, after generally outperforms. The proportion of months with positive controlling for expiration effects. Second, and importantly, excess returns in non-expiration months also greatly exceeds the coeffi cients on the expiration dummy variable suggest that that in expiration months. These results suggest that the the synthetic position appears to signifi cantly underperform synthetic position outperforms the accumulation index in non- by between 31 and 56 basis points in expiration months expiration months, in fact, in almost two-thirds of the months (depending on the rollover date). examined. This could be due to the ability of the synthetic Interestingly, one of the implications of the results is that position to deliver the value of franking credits to investors franking credits are priced into stock index futures contracts (which are not included in returns based on the S&P/ASX200 despite the introduction of the 45-day rule in July 1997, which Accumulation Index). A repeat test of the relationship between seemingly appear to prevent this. Under the 45-day rule, the synthetic return and the franking credit yield of the index investors not holding stock continuously for 45 days around follows. dividend payment periods are not entitled to franking credits14. Additional tests If the 45-day rule is adhered to there should be no positive relationship between the return on the synthetic position If arbitrageurs are able to extract dividends as well as a and the franking credit yield. Arbitrageurs would not be proportion of franking credits from the index portfolio when entitled to franking credits on stocks held for less than holding an arbitrage position, the capital gain on the futures 45 days and subsequently could not price them into the futures and hence the outperformance of the synthetic position relative contract. However, there is anecdotal evidence suggesting to the accumulation index should be higher in months where that arbitrageurs are able to avoid the 45-day rule and extract franking credits are higher. In order to test this proposition, the value of franking credits through carefully constructed while controlling for transaction costs associated with rollover transactions15. In the presence of such transactions there in expiration months, the following regression model was exists plausible justifi cation for the pricing of franking credits estimated: into futures contracts and a positive and signifi cant relationship rbrbfbEe . between a synthetic portfolio and franking credit yield. Where: pt,1,2 AIt t 3 t t The empirical evidence provided by this paper is therefore r is the return to the synthetic position in month t consistent with anecdotal evidence of avoidance of the 45-day p,t rule.

rAI,t is the monthly return to the accumulation index in month t 5. Summary And Conclusion This paper proves mathematically that returns on synthetic ft is an estimate of the franking credit yield on the accumulation index in month t positions using stock index futures contracts and a ﬁ xed income security should deliver capital gains as well as the

Et is a dummy variable equal to one if month t is an expiry value of dividends derived by arbitrageurs. Consistent with month, otherwise zero. this proposition, the empirical evidence provided in this paper The franking credit yield was estimated by taking the reveals that a synthetic position comprising a long position difference between the accumulation index return and the price in a stock index futures contract plus a bond, delivers the index return to obtain the dividend yield, which was then value of capital gains and dividends, plus a proportion of the grossed-up, assuming a corporate tax rate of 30 percent and value of franking credits. This is despite the provisions of that all dividends in the index portfolio were fully franked. the Income Tax Assessment Act (specifi cally, the 45-day rule), which intend to prevent arbitrageurs from obtaining Estimates of the model above can be used to assess the value of franking credits and consequently pricing them whether the return on the synthetic position delivers the value into the futures contract. The results also highlight that the of dividends and capital gains, in which case the coeffi cient adverse performance of the synthetic position in expiration should be close to one. Also, whether the return on the months potentially negates any outperformance achieved in synthetic position is related to the franking credit yield of non-expiration months. The rollover strategy used is therefore the index can be assessed by examining b2, which should a key factor in unlocking the full benefi t of synthetic positions be positive and signifi cant if arbitrageurs can extract the involving index futures. The fi ndings in this paper also suggest value of franking credits from the index portfolio. Any that previous research which assesses the tracking effi ciency of underperformance during expiration months is captured in the stock index futures contracts against price indices need to be coeffi cient b3. revisited - returns from synthetic exposure need to be assessed Table 2 sets out the results of the analysis. As expected, against accumulation indices. the coeffi cient b1 is approximately equal to 1 and highly signifi cant for all rollover dates, consistent with the proposition that the synthetic position delivers the value of dividends in addition to capital gains. Two other very important results are reported in Table 2. First, there is evidence that the relationship between the performance of the synthetic position and the franking credit

12 Journal of Law and Financial Mangement - Volume 3, No. 1 Returns on Synthetic Portfolios

References 9. Analysis using reported futures closing prices revealed that tracking error would be overstated by a margin of up * Alex Frino is ccorresponding author and a Professor of to 17 basis points. Finance at the University of Sydney. Postal: Finance Discipline, Building H69, University of Sydney, NSW, 10. Christopher Ma, Jeffrey Mercer and Matthew Walker, Australia, 2006. Telephone: +61 2 9351 6451. Fax: +61 “Rolling Over Futures Contracts: A Note” (1992) 12 2 9351 6461. E-mail: [email protected]. Grant Journal of Futures Markets 203-217. Wearin is a doctoral candidate at the School of Business, 11. The return on the fi xed income component of the synthetic University of Sydney and Joel Fabre is an associate lecturer position is adjusted for each rollover date. For example, at the School of Business, University of Sydney. a rollover occurring on day T-20 uses the BAB yield from 1. Phil Holmes, “Stock Index Futures Hedging: Hedge Ratio twenty days prior to the futures expiry date. The BAB Estimation, Duration Effects, Expiration Effects and Hedge yield is updated on rollover. Ratio Stability” (1996) 23 Journal of Business Accounting 12. Analysis using rollover dates of 1, 5, 15 and 20 days prior and Finance 63-77. to expiry produced similar results. 2. Martin Gruber, “Another Puzzle: The Growth in Actively 13. Alex Frino and Michael D. McKenzie, “The Pricing Managed Mutual Funds” (1996) 55 Journal of Finance of Stock Index Futures Spreads at Contract Expiration” 783-810; Alex Frino and David Gallagher, “Tracking (2002) 22 Journal of Futures Markets 451 - 469. S&P 500 Index Funds” (2001) 28 Journal of Portfolio Management 44-55; Alex Frino and David Gallagher, “Is 14. Days where a risk-reducing transaction or arrangement Index Performance Achievable?: An Analysis of Australian are in place (i.e., transactions related to hedging) are not Equity Index Funds” (2002) 28 Journal of Portfolio counted as part of the 45 days. Under the 45-day rule, a Management 44-55. maximum delta of 0.7 for delta style hedges is allowed. 3. The fi rst stock index futures contract, covering the Value 15. Stuart Washington, “Not Guilty Says Macquarie” (2003) Line Index, was listed by the Kansas City Board of Trade 25 Business Review Weekly 22. in February, 1982. All Ordinaries index futures were listed by the SFE in February, 1983. On May 2, 2000, the SFE listed SPI 200 futures to refl ect the change to the S&P/ ASX 200 as the broad-based benchmark. 4. John Fleming, Barbara Ostdiek and Robert Whaley, “Trading Costs and the Relative Rates of Price Discovery in Stock, Futures and Option markets” (1996) 16 Journal of Futures Markets 353-387; Lorne Switzer, Paula Varson and Samia Zghidi, “Standard and Poor’s Depositary Receipts and the Performance of the S&P 500 Index Futures Market” (2000) 20 Journal of Futures Markets 705-716. 5. An earlier version of this paper was workshopped amongst fund managers. We were surprised by the large number of managers that initially held the view that because the SPI 200 futures contract is settled against a price index, a synthetic position would not deliver dividends (let alone franking credits). 6. Stephen Figlewski, “Hedging Performance and Basis Risk in Stock Index Futures” (1984) 39 Journal of Finance 657-669; Phil Holmes, “Stock Index Futures Hedging: Hedge Ratio Estimation, Duration Effects, Expiration Effects and Hedge Ratio Stability” (1996) 23 Journal of Business Accounting and Finance 63-77; Juan Lafuente and Alfonso Novales, “Optimal Hedging Under Departures from the Cost-of-Carry Valuation: Evidence from the Spanish Stock Index Futures Market” (2003) 27 Journal of Banking and Finance 1053-1078. 7. Allan L. Tucker, “Financial Futures, Options and Swaps”, 1991, pp. xx - yy. 8. The S&P/ASX 200 was fi rst introduced on March 31, 2000. We begin our analysis from September 1, 2001 to avoid the unusual expiration effects in June 2001, where an alleged manipulation of the SPI 200 occurred on settlement (Jemima Whyte, “ASX Fines Broker for Breaking Rules” (December 17, 2002) Australian Financial Review).

June 2004 13