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If you look at a cumulative return of a very simple portfolio, consisting of long EuroStoxx50 total return index and short EuroStoxx50 futures, you can see that over the last 10 years this portfolio accumulated c.15% of return.

In theory, return of this portfolio should be equal or very close to a risk-free return. But when you look at a cumulative return of 3M Euribor, you see that over time the above-mentioned portfolio strongly outperforms this 'risk-free benchmark'.

Why is it the case?

PS. I accounted for the roll-over Fridays and subsequent Mondays by excluding returns on those dates.

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  • $\begingroup$ I'm not sure excluding returns on Friday and Monday is the proper way to deal with the futures roll. But perhaps I misunderstood what you did. $\endgroup$
    – nbbo2
    Commented Jan 12, 2018 at 13:14
  • $\begingroup$ why? I mean, I don't argue that is a completely correct way of dealing with it, but it definitely makes the time series more smooth and excludes the rollover jumps. I surely could have inserted levels from VG2 Index for the last several days of futures' life, but is it worth of efforts? (for this case I used the VG1 Index time series) $\endgroup$
    – Lina
    Commented Jan 12, 2018 at 14:52
  • $\begingroup$ Since you are using Bloomberg I recommend you check the CDEF command to see if you are using adjusted or unadjusted series for VG1. I recommend you use adjusted series, which will have no rollover jumps, the rollover adjustment will be done correctly by Bloomberg. $\endgroup$
    – nbbo2
    Commented Jan 12, 2018 at 15:02
  • $\begingroup$ Do you think the SX5EFETR Index would do instead? $\endgroup$
    – Lina
    Commented Jan 12, 2018 at 15:19

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Small details accumulated over 10 years will explain the discrepancy. You need to simulate the actual strategy i.e. include cost of funding the long index leg, cost of margining the futures leg, replicate the index roll properly (create a composite rolled-future index where the 3rd Friday return is VG1(Friday close) / VG2(Thursday close) - 1 and take the bid-ask of the roll into account (assume 1 euro).

The performance over 10 years then will be generally flat, with positive and negative periods and no obvious arbitrage.

I don't know how SX5T is calculated top of my head but the reinvested divs are almost certainly at a tax rate (either worst-case tax rate or zero) different from that implied by the futures price (which reflects an "average" (in some sense) tax rate of participants). That will also explain part of the difference. In reality you won't have that exact tax rate on your SX5T holdings.

Finally by trading the future you run dividend risk, it is small as it's short-dated, but it exists. You don't on your SX5T leg.

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  • $\begingroup$ Thanks for the detailed answer! I used in my calculations the SX5GT Index rather than SX5T... Am I right to think that Total Return version would overestimate amount of dividend returns for reinvestment in comparison to futures, while the Net Return version would sort of underestimate this amount? So, roughly speaking, portfolio with TR Index would generate higher returns than a NR portfolio? $\endgroup$
    – Lina
    Commented Jan 15, 2018 at 8:04
  • $\begingroup$ Yes, that is a fair assumption $\endgroup$
    – Ivan
    Commented Jan 16, 2018 at 8:47
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From a mathematical perspective and under the capital market assumptions of finance theory, you would be right. However in real life, there are a number of risks that remain that keep this from being a risk free return.

Among these risks are dividend risk, taxes and tax risk of different investors, interest rate risk and central bank policies, inter and intra country regulatory risk, capital requirements of individual market makers, roll risk etc.; as well as transactions costs. Market participants assess these risks and price it into the markets.

There is almost never a truly risk free arbitrage.

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  • $\begingroup$ Thank you for your answer! What is surprising me though is the size of this discrepancy. I manage to mitigate it at least to some extent by incorporating with Euribor a 3m ECB Repo Rate, but I don't know whether it is a correct approach.. $\endgroup$
    – Lina
    Commented Jan 12, 2018 at 15:35
  • $\begingroup$ Another point to mention is that if I am looking at an annualized standard deviation of this portfolio, i.e. std(Return(Index) - Return(Futures))*sqrt(252), it appears to be around 2.7%. I understand that because of the supply/demand issues, existence of basis, etc. this volatility would never be close to 0. But I am still wondering if it is not too much for a seemingly perfectly hedged portfolio? Finally, I am not sure whether Futures takes into account a withholding tax on the dividends? And if it does, should I rather use a Net Return version of EuroStoxx50? $\endgroup$
    – Lina
    Commented Jan 12, 2018 at 15:38
  • $\begingroup$ Repo is a step in the right direction in that you are looking at a market rate that collectively participants are using to finance the trade. This rate is a blended rate that takes into account all of the risks in my answer and then some. Most use a fair market value driven from the risk free rate and then make their own adjustments taking into account their unique circumstances. With respect to div taxes, the net taxes would be the correct but whose tax rate? Again each will use their own situation and the price will be a blend of those in the market at that time. $\endgroup$
    – AlRacoon
    Commented Jan 12, 2018 at 16:01
  • $\begingroup$ Am I essentially right to think that in real-life circumstances it is impossible to expect that the above-mentioned volatility could be as negligible as 0.5-1%? My problem in this case is that then I don't know how to measure quality of my hedging if I do the same to other indices which do not have direct futures using exactly these indices as underlyings... Because in this case results can be even worse $\endgroup$
    – Lina
    Commented Jan 12, 2018 at 16:14
  • $\begingroup$ I'm not an active participant in this market so I am not sure how low you can expect to get the volatility of your position down. It probably fluctuates from time to time, when you place your position (near div payouts etc) and for how long your hedge is your (how many times you need to roll). I suppose you can use your calculation as an estimate of the best you can expect to achieve in hedging positions without a direct futures market. The more basis risk you have between your hedge and your position would make it more volatile (all else equal). Sorry I don't have a more definitive answer. $\endgroup$
    – AlRacoon
    Commented Jan 12, 2018 at 16:29

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