Interest Rate Arbitrage in Negative Yielding Currencies

Arbitrage example using Swiss Franc options

Originally published in the issue

In a world of negative interest rates and growing risk for asset price bubbles everyone is seeking new high yield/low risk opportunities. One might be based on the weird situation that banks pay deposit rates which are above the inter-bank lending rates. This offers a possibility of arbitrage in CHF and EUR especially for wealthy private investors with a sizeable bond or equity portfolio.

1. Idea
The idea is very simple. Get a loan with negative interest rates, use your bond or equity portfolio as collateral and deposit the capital that you get from the loan for an interest rate of zero. The result is that you’ll get interest for theloan (because of the negative interest rates) and you’ll get and pay nothing for the deposit. Ideally you even receive interest on your deposit and you can leverage this deal 10+ times and you will earn a high return with a low risk profile, but let’s see how the trade works.

2. Implementation
a) Taking up a loan with negative interest rate

The main question that I asked myself at the beginning of the construction of this arbitrage deal was: how to get a loan with a negative interest rate as a normal retail customer. Based on my experience as a derivatives trader I finally came up with the idea to use a “box”. A box trade is a combination of European style options which are combined in a way that they deliver a zero coupon bond return. That means that the only price risk that remains is an interest rate risk. Delta, Gamma and Vega are zero and only Theta and Rho remain. If the box is traded as a short box then it works like the issuance of a zero coupon bond (equivalent to taking up a loan with fixed interest rate and one bullet payment at maturity). A “short box” consists of a sale of one in the money call and one in the money put and the purchase of one out of the money call and one out of the money put. The short call and long put have the same (low) strike and the short put and the long call have the same (high) strike (see example below). As a result, by selling a box you receive cash. The amount of cash equals the difference of the two strikes times the option multiplier (“nominal amount”; multiplier e.g. 10 for Eurex EuroStoxx 50 or SMI Index Options) less the interest value of the option. This equals exactly a zero bond, which is traded at its nominal less a discount for interest. As the interest rate that is incurred in the pricing of a box is negative the price of the box is higher than its nominal amount. That means by selling a box you receive the nominal amount plus interest and you only have to pay back the nominal amount. So finally by selling a box you effectively take up a loan with a negative interest rate which leads to the fact that you have to repay less than you receive initially. That’s how negative interest rates work.

b) Use of leverage
Obviously for getting a loan by selling a box and receiving cash your broker will ask for margins. In case of using SMI-Index derivatives EUREX requires about 103% of the daily settlement prices of the box as margin. So let’s assume that your broker takes no additional margin, that means that for every box worth 100 CHF you need 103 CHF Cash1 to meet the margin requirements (see example). Fortunately, by selling a box we already received cash of 100 CHF. This means that we only need additional 3 CHF of equity for each trade and this means that we have created a leverage of 33!

In practice, you have to deposit the full amount of margin required for one box trade first and then you can start trading. Nevertheless, you can then increase the leverage by trading 33 boxes in total. As you in fact only need equity in the amount of 3% of the net premiums, you can use your initial 100% of equity to successively increase the leverage by trading one box after another until you’ve reached the maximum leverage of 33. The result is the same. For my trade, I financed my initial equity with a CHF mortgage loan from another bank. So I had an almost infinite leverage in total but the interest payments for the loan lowered my return. Anyway, let’s look at the trade without the double leverage structure.

c) Return
As described in the example, one box will deliver a return of 482 CHF after fees before tax. In relation to the injected equity of4,516.50 CHF this leads to a return on equity of 10.67% which equals 21.5% p.a. The condition for achieving this return is that your deposited margins are yielding 0% during the lifetime of the whole trade. If the yield is higher, the return is even above 21.5% and vice versa.

3. Risks
a) Counterparty risk

There are two counterparty risks involved in this trade. First there might be a counterparty risk in relation to the broker/Eurex. Obviously as we are taking up a loan by selling a box and we are assuming netting as we trade all options through the same broker there is no such counterparty risk. The broker/Eurex requires a margin because they are bearing the counterparty risk.

The second counterparty risk is related to the deposit. Usually, a private client benefits from deposit protection which might be lower than the margin that you have deposited. In addition, in case of an insolvency of the broker, you will have a claim against the broker in form of your deposit and the broker has a claim against you in form of the open box trade. Whether both can offset each other, depends on the local insolvency regulations. Anyway you should look for a broker which is solvent, has a good rating and offers a high deposit protection. Additionally, if you can use your equity or bond portfolios as margin then you can make some smaller deposits with different banks. This diversifies the credit risk.

b) Increase of margin
If you have enough equity (e.g. in form of your bond/equity portfolio) to meet any margin call no matter how high, then a margin increase poses no risk. A deleveraging by delivery of additional margin will not affect your total return in CHF but your return on equity in %. It goes down as you have delivered additional equity in form of additional collateral. If you don’t have enough equity to meet any margin call with additional equity then there is a risk of increasing margins and a risk of forced deleveraging by closing some of your box trades. There are three reasons why margins could be higher than expected. Firstly, Eurex could increase their margin requirements due to a new margin framework or higher risk parameters. Keep in mind that a box doesn’t contain any volatility risk and that the value is not dependent on the price of the underlying. Just a high volatility in interest rates can lead to higher margin requirements. As far as I know, the current margin parameters are still based on the extreme short term interest rate movements during the Lehman crisis, which is, in my opinion, a worst case scenario. So the margin parameters are already very high and to me it sounds unlikely that they could be even higher. Nevertheless, I considered an additional buffer of 0.5% equity as sufficient. This reduces the maximum leverage to 28.

Secondly, the broker can increase its margin requirements. This is less foreseeable than the changes imposed by Eurex. In theory that means that we should increase the buffer. But as we don’t have any idea upfront how the broker could adjust its margin requirements I didn’t use a buffer for this risk. I took the residual risk as the increase of margin requirements would lead to deleverage in form of injecting additional equity or in the unwinding of some box trades to be compliant with the margin requirements.

Thirdly, market movements of interest rates result in a higher or lower fair value of the box, creating “mark to market” risk prior to maturity. Lower fair values lead to lower margins and thus could release further equity. Higher fair values lead to higher margins but as we earn negative interest every day during the lifetime of the box the risk of higher fair values in relation to the initial fair value of the trade is quite limited. My trade had a lifetime of about 6 months. To have the same residual fair value of the box after 3 months, the negative interest ratesimplied in the box had to double! So time is a good hedge against increasing fair values and thus against higher margins (Fig.1 and Fig.2 show the effect of time decay on the risk profile of a 1-year trade). I decided that the 0.5% that I’ve reserved for the possible increase of the Eurex margin requirements can cover the risk of increasing fair values as well.

c) Deposit rate
The deposit rate is the weakest part of the trade. Remember, we are receiving cash with a fixed interest rate by selling the box. Now we have to somehow invest this cash and ideally in a way that it is eligible as collateral and delivers a high but fixed return. There are two options. The first one is to buy bonds or equities which may offer a high return. I didn’t choose that option because returns are not fixed as you have a price risk and you may not find bonds with an identical term as the box to avoid the price risk so that suddenly your collateral has too little value. Even more important for me was the fact that the value of bonds and equities is usually not fully recognized as margin. You’ll have to accept huge haircuts. That led me to the second option, a deposit. If you have the chance to make a term deposit with the same term as the box and with a higher interest rate than the box, then this would be the perfect trade. With a term deposit you can eliminate totally the residual interest rate risk as you fix your interest income and you’ve already fixed your interest payments with the short box. In my case in CHF it was not possible anymore to make term deposits but a deposit with daily liquidity was still offered with an interest rate of 0%. The flipside of the daily liquidity was that the interest rate could have changed any time. A negative interest rate would have lowered my return but the break-even rate was -0.63% p.a. which offered quite a good buffer for that risk. The worst case scenario is that the deposit rate is below the rate of the box, then you should think about a total unwinding. Therefore, I would recommend to set up the arbitrage with an initial tenor of 6 to 12 months. This helps to reduce price volatility of the box trade, which is important for a case of forced unwinding.

d) Execution risk
If you have full access to the Eurex trading facilities then there is no execution risk as you can trade the box as strategy. That means that one order includes all four options and they will all be executed at the same time. My broker didn’t provide a trading system for strategy trades so I had to trade option by option. This includes an execution risk as one option may be executed and the rest are not while the underlying is moving fast. So I decided three things:

  1. I chose the biggest difference of strike prices possible. This reduces the impact of market movements because a 1 point market movement equals 10 CHF change in premium. 10 CHF in relation to 150,000 CHF nominal (=difference of strike prices x multiplier) per box is far less than in relation to let’s say 10,000 CHF nominal. A nice side effect is that a high nominal value per trade reduces your transaction costs as you have to trade less options.
  2. Trade the short options, the deep in the money options, first as they determine the success of the trade. And try to get them executed at the same time to avoid any market risk (their deltas are offsetting each other). The two long options have no high premium and only a very low delta and vega. So they can be traded later.
  3. As it is very unlikely that both deep in the money options will be executed contemporaneously, try totrade the deep in the money call first. This offers protection for unexpected sharp downward movements of the underlying during your execution. My assumption was that a sharp downward movement is more likely than a sharp increase of the underlying price.

e) Taxes
Tax issues are always individual and always different. Before setting up the trade ask your tax consultant what the implications in your jurisdiction are. For example, for tax purposes I had to found a limited company to secure the netting of all returns and all costs, as the tax calculation for this trade for me as an individual in Germany doesn’t follow the economic result at all.

5. Summary
Simple idea, low risk/high return profile but risk management is crucial. For me the most difficult part was to find a broker where margin requirements were as low as the original Eurex margin requirements. Only that enabled a high leverage. For investors with huge equity/bond portfolios the question of margin requirements may be less important as they can use their existing portfolios as margin. You should then focus on credit quality of the deposit, possibilities to make term deposits and execution risks. Other trades consisting of bond or equity futures combined with deposits instead of holding bonds or equities are also possible. And then let’s arbitrage banks and brokers.


1. As far as cash is counted without any discount. Some Brokers take a haircut on cash deposits which economically only makes sense if the cash deposit is held at another bank. A haircut on deposits held with the broker would indicate that the broker doesn’t trust its own creditworthiness.

• 23 years in banking/investment industry. Diploma of Business Administration, Eurex trader, entrepreneur.
• 2002-2010 Department Head of Trading and Investments with 3.5bn AuM, Kreissparkasse Köln, Cologne.
• 2010-2012 Partner at Antecedo Asset Management with 1bn AuM in option based strategies, Bad Homburg.
• 2012 – today Senior Investment Manager “Strategic Projects”, DEG, Cologne