### Heads I win, tails you lose: Valuing a callable note

This week we examine callable structured notes. Our representative note and its terms can be found here.

*Why are we interested?*

Notes with a call feature typically offer very attractive “headline” yields, but these structures often aren’t as attractive as they may first appear. Generally, they are worth significantly less than a non-callable note with the same features and yield. **In today’s Deconstructed Notes, we will demonstrate why the analyzed callable note that legitimately markets a 15% annual yield is in fact economically equivalent to a 7.35% yield when not callable. A call feature enables a higher “headline” yield because it introduces a chance that the higher yield is not paid; generally, the probability-weighted interest cost to the issuer is the same as a non-callable note. **

Consider the following scenario…a person pays $1500 a month for an insurance policy guaranteeing annual medical coverage. Because the person is generally healthy, the insurance company pays out significantly less than $1500 a month in medical bills and is making a profit each month. Suddenly, things change and the insured comes down with a serious illness. The medical bills will now cost the insurer more than $1500 per month. The insurer exercises a clause in its contract stipulating that it can cancel the policy. A sweetheart deal for the insurer, no?

While this scenario is an oversimplification, it offers some important lessons when considering structured notes with call features: Namely, that when the deal is in favor of the investor, the issuer has an out ** **

**Now, let’s get into the details:**

*Terms of the trade*

The general terms of the issue are as follows:

- 2 year note
- Quarterly coupons of 3.75% (annualized at 15%) as long as HTZ is not below $15.50 on the coupon date. $15.50 represents 70% of HTZ’s value on issuance date ($22.14). If HTZ is below $15.50, investor receives no coupon for that period.
- For example, if HTZ closes $16 on a coupon date, investor receives 3.75%. If HTZ closes $15 on a coupon date, investor receives 0%.

- At maturity, if HTZ closes above $15.50, investor receives return of principal; if HTZ closes below $15.50, investor receives the return of HTZ.
- For example, if HTZ closes $16 at maturity, investor receives original principal back in addition to coupon (from above). If HTZ closes $15, investor receives 67.8% of principal back ($15/$22.14) and no coupon.

**Early Redemption Feature: issuer can call the note on any coupon date for par.**- For example, after one quarterly payment of 3.75%, the issuer decides to call the note and return principal. The note would cease to exist and investor would generate a 15% return for one quarter.

*Technical Breakdown – Contingencies and Call Options*

If the investor received all eight quarterly coupons of 3.75% with no contingencies and no callable option, the expected yield of the payment stream would be 15% per annum. *However*, these are contingent coupons – they are only paid if HTZ is above a certain minimum. In addition, this note is callable – if HTZ is performing well and it seems likely the issuer will be “stuck” borrowing investor money at 15% per year, the issuer is likely to call the note.

So what is the actual value of the payment stream when the contingency and callable features are both taken into account? The short answer is approximately only 6.4% per annum, less than half of the potential yield described in the term sheet! If the contingency feature is removed, leaving only the callable feature, the actual value is 7.35%.

The mathematical proofs behind the 6.4% and 7.35% follow. We approached the valuation by essentially separating the values associated with the investor position in this trade from those of the issuer position. Let’s review those elements:

**Investor coupons:**

Each quarterly coupon due the investor has a probability level of being paid based on the odds of HTZ not declining below $15.50 as of the coupon payment date. The value for the investor is the present value of this coupon stream.

**Issuer “knock-in” option:**

The issuer benefits from the value of the potential payout if HTZ closes below $15.50 at maturity (i.e., the issuer’s option “knocks in” if HTZ closes below $15.50). This value is equal to the probability of this occurring multiplied by the average value of the occurrences.

**Issuer call option: **

With the values for each party now identified, the question becomes when will the issuer be compelled to call the note? Well, if the value to the investor is higher than the value for the issuer, it makes sense to call the note. For example, if the investor benefit of the stream of coupons is worth $5 and the issuer benefit based on the probability and value of a decline below $15.50 is $4, the issuer does better to simply redeem the note and save $1 ($5 – $4). Conversely, if the investor benefit is $4 and the issuer benefit is $5, the issuer does better to wait another period and monitor the valuation at the next available redemption date.

The term sheet indicates the structured note is worth 96% at issuance. Assuming the Zero Coupon bond is worth ~98% (which reflects the yield a typical issuing bank would be expected to pay), then the remaining components of the note structure — the coupon payments to the investor and the knock-in option to the issuer — are worth 2%. Thus, if the knock-in is worth X%, we know the stream of coupons due the investor is worth X% – 2%. Now, let’s solve for these missing variables.

*A Little Help from Monte Carlo*

Specifically, I am interested in deconstructing the investor coupon to understand the affects of

(1) the contingency where an investor does not get a payment on a coupon date due to HTZ closing below $15.50;

(2) the Issuer Call Option.

Both of these elements reduce the probability of the investor being paid the full 30%. When you strip these two elements away, what’s left is a stream of coupon payments and the issuer knock-in option.

I had a trusted associate run a Monte Carlo simulation 2,500 times to ascertain the value of the yield contingency and call feature. Note that a Monte Carlo takes into account the general market characteristics as applied to HTZ and simulates an outcome over and over again. Run enough times, it provides the value of the payouts.

**Understanding the impact of the yield contingency:** My Monte Carlo simulation indicated the present value of the investor’s position was 26.1% based on the likelihood of receiving most of the coupons over two years. The difference between a 2 year value of 26.1% and a straight line value of 30% (8*3.75%) is the effect of the yield contingency – 13% of the expected yield value is lost due to the fact that in some quarters a payment won’t be made due to HTZ falling below the threshold. (Note these values do not take into account the callable option feature; that is coming soon!)

So now we have the effect of the contingency. If there is no contingency associated than the equivalent value of the 30% yield (15% per annum) would be 26.1% (13.05% per annum). I have effectively stripped out that component. How about the Issuer call option?

**Understanding the impact of the call feature:** Using the same Monte Carlo, the value of the issuer knock-in option is 14.8%. I had mentioned above the fact that the stream of coupons is worth the issuer knock-in option less 2%. That means that if the coupons had a 100% chance of being paid, with no contingent payment feature and no call, the stream of coupons would be worth 14.8% – 2%, or 12.8%! This comes out to a **6.4%** per annum yield. Note this 6.4% yield is mathematically equivalent to each of the following yields and scenarios:

**7.35%**per annum yield if there was a contingent payment feature but no call feature (as discussed above, the contingent feature removes 13% of value; to reverse that, divide 6.4% by 87%)**13.05%**per annum yield if there was a call feature but no contingent payment feature**15.00%**per annum yield if there is both a contingent payment feature and a call feature

This is all due to the weighting of probabilities to the different yields. Stated differently, if receiving the coupon of 6.4% is 100% probable, then receiving 15% per annum (when the coupon includes the issuer call option and contingency) is 42.5% probable (15% * 42.5% = 6.4%).

As can be seen in the table above, I have just defined 4 different popular products in the SP industry allowing for a good starting point in understanding the impact of a product feature. As a side note, an Autocall note is pretty similar to a callable but perhaps we will focus in on that sort of a note in a future blog.

**How can the call feature be so impactful?**

The following graph illustrates 10 random simulations of HTZ performance over a 2 year period. The X axis is time and the Y axis is the value of HTZ. As you can see, in scenarios where HTZ performance is sufficiently positive, the note is redeemed early (the line ceases to exist). In scenarios where the issuer is favored, the note is not redeemed and the note continues for the full 2 years. The takeaway from this chart is that in the majority of cases, the note is called shortly after issuance (in fact, 75% of the time it is called after the first quarter).

*Takeaway*

In summary, the issuer call option is actually quite valuable and will materially affect the yield provided to the investor. The graph above is a vivid illustration of the performance of notes with call features. So while it’s exciting to consider collecting 15% per annum for two years, the more likely outcome is that this note would generate a 15% yield for exactly three months!! If the note is not redeemed after three months it probably means HTZ is performing poorly, the issuer knock-in option comes into play, and the yield, once again, is not what it would seem! **To be certain, we are not suggesting that investors should run the other way whenever a callable note it presented; rather, our aim is to make sure that investors enter such trades with an understanding of how the notes are constructed, and with a better idea of what their actual return is likely to be. **