Introduction to Merger Arbitrage and Interest Rates
Interest rates play an integral role in finance. A given interest rate will find its way into almost all financial calculations and valuations. The relationship with between merger arbitrage and interest rates however is a little more subtle. A pure merger arbitrageur does not claim to be able to forecast or even have an opinion on the future interest rate level. However, to be oblivious to its effect in the calculation of the merger arbitrage spread would financial folly. This article explains how understanding the effect of interest rates can improve the profitability of your merger arbitrage trading. See our guide how to profit from merger arbitrage for additional trading tips.
- Why interest rates are important in merger arbitrage
- The effect of interest rates on merger arbitrage profitability
- How arbitrageurs can improve the profitability of a merger arbitrage strategy
The Importance of Merger Arbitrage and Interest Rates
According to the Bank of England,
“An interest rate is a percentage charged on the total amount you borrow or save.”
Therefore, if the one-year interest rate (IR) is 10 %, and you borrow $100 for a year, the total repayment would be
$100 + $100 * 10% = $110 (1)
So, the higher the interest rate, the more expensive it becomes to borrow. Now, by simply reversing (kind of) this equation, we can calculate what the present value of $100 is in one years’ time
$100 / (1 + 10%) = $90.91 (2)
In other words, if we could loan (or invest) $90.91 right now, for exactly one year, at a rate of 10%, it would be worth exactly $100 at the end of the period. In this case, we know the target price or realisation value of an investment in advance. Therefore, a higher interest rate implies a lower initial price of the investment.
Without any change in fundamentals, changes in interest rates, anticipated either in the open market or via central bank actions would affect the prices of assets. It is irrelevant at this point whether or not market participants consider rates “high” or “low”. It is the change in rates from this level, over the life of the investment that will affect its value.
Interest Rate Duration
When assessing investments, one of the obvious problems that spring to mind when discussing interest rates is the choice of interest rate. Short, medium and long-term rates all have their unique characteristics. Clearly, they have different values and levels of volatility. In merger arbitrage, deals rarely take longer than 6 months to complete. In fact, we previously analysed cash only mergers and acquisitions and found the average completion time was between 4 and 5 months. It is therefore wise to use an interest rate with a commensurate length of time when valuing merger arbitrage spreads. Tender offers tend to complete faster. Stock swap transactions tend to be larger and involve more regulatory complexities and can therefore take a lot longer. At the time of writing, the 6-month T-bill rate was 1.83%. We will be using this rate throughout the remainder of this article.
The Effect of Interest Rates on Merger Arbitrage Profitability
It should be clear to the reader how interest rates fit into the profitability calculation. The trader knows in advance the final value of the investment. (Assumption #1, there is no higher offer made during the merger process). This is the offer price. From the previous section, we know how mergers with similar characteristics complete the deal in similar timeframes. Such as, tender offers, or smaller acquisitions not subject to regulatory oversight will tend to complete quicker. (Assumption #2, there are no subsequent issues delaying the closing of the deal).
An Example
Let us look at Waste Management’s (WM) acquisition of Advanced Disposal Services (ADSW). The initial announcement of this deal was in April 2019. The initial announcement stated the expected closing of the deal would take place in the first quarter of 2020. At the time, the 1-Year Treasury Constant Maturity Rate interest rates was 2.43%. The offer price was $33.15 per share. Our studies have shown this deal would most likely complete around the end of 2019. In which case, we calculate the 9-month interest rate (9 months / 12 months = 0.75) as follows
(1 + 2.43%) ^ 0.75 – 1 = 1.82% (3)
Let us plug this data into equation 2.
$33.15 / (1 + 1.82%) = $32.56 (4)
Assumption #3, there is a 100% the deal will close as expected. Assumption #4, there are no dividends or additional capital payments scheduled. Clearly, assumption #3 is unrealistic but before we tackle this, let us look at the output. The current theoretically discounted price is $32.56. This means that any observed market price above this level will produce an inferior return to simply holding cash. It is important to remember this is the theoretical price calculated at time0. As time moves on and the expected closing date approaches, the effect of the interest rate is reduces and the stock price increases. Much the same way the value of a cash deposit increases as interest accrues.
Improving Merger Arbitrage Profitability
Let us quickly review our assumptions so far,
- #1, there is no higher offer made during the merger process
- #2, there are no subsequent issues delaying the closing of the deal
- #3, there is a 100% the deal will close, as expected
- #4, there are no dividends or additional capital payments scheduled
The value of $32.56 can be seen a clean price from which we can build upon. If all four assumptions hold, there are no further calculations necessary. The arbitrageur simply decides how much of a premium they are willing to receive over and above the prevailing inters rates to bear the risk of the deal not closing. For example, if the stock were trading at $32.50, would taking on the risk of deal failure be worth $0.06? Probably not.
Assumptions #1 and #4
Assumptions #1 and #4 have a positive impact on the stock price if they become relevant. These are coloured green for your convenience. If either of these two assumptions apply, the stock may legitimately trade above the $32.56 base price. The reverse can also be a possibility for Assumption #1. This was the case with BassPro’s (BASS) takeover of Cabelas (CAB). The initial offer of $65 was subsequently reduced to $61.50. However, this simply means recalculating the equation and arriving at a new clean price.
Assumption #2 and #3
Assumption #2 and #3 have a negative impact on the stock price if they become relevant. Assumption#2 is a real possibility in larger complex deals where the parties involved have underestimated the timings or possibilities of additional regulatory issues. Political issues such as the ongoing trade war with China have effected deals such as Mellanox (MLNX) and Acacia (ACIA) amongst others. Factors such as these significantly complicate the expected deal-closing timetable. In this case, the arbitrageur needs to revise the closing date using experience and available information. The trader the computes the calculations using equation 4 once again. It will of course be necessary to update the appropriate interest rate given the change in the closing schedule.
Assumption #4 is where most traders lose sight of the effect of interest rates on merger arbitrage profitability. The Deal Closing Probability (DCP) changes constantly and is not always readily observable in the market. Should assumptions #1, #2 & #4 hold, the underlying stock price should never reach $32.56 at time0. The level of uncertainty of deal completion is what causes the majority of the spread. If the stock were trading at $32.50, it would imply the deal is almost certain to close.
Masking Effects of Additional Inputs
The market may or may not be correct in this analysis. Perhaps there has already been a positive shareholder vote and all regulatory blessings have been forthcoming. In which case, a $0.06 may induce the trader to make an investment. (If this were the case however, it would be unlikely there was still 9 months before expected deal completion). The cost of foregoing putting funds on deposit needs to be part of the profitability analysis.
What at first may look like a large spread may simply be the product of high interest rates and an extended deal closing timeframe. If rates are already low, rising rates can therefore cause a spread to widen, as investors require a greater return. Traders already with a position will see a loss as the stock price declines. This loss has nothing to do with the DCP. This input may or may not be changing simultaneously. Since the end of May 2019, short-term interest rates have declined by over 0.50%. However, many traders and news outlets were unable to distinguish this from the underlying performance in merger arbitrage.
Conclusion
It is important to understand the (relatively) fixed nature of the interest rate portion when calculating the merger arbitrage spread. In this case, the arbitrageur will be less likely to over pay to be part of the deal. Instead, it may be wise to leave funds on deposit until better opportunities present themselves. Likewise, the trader should be aware when profits are attributable to a change in interest rates or to a change in the probability of a successful deal closure.
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