Preferred Stocks Live Longer Than Bonds, But Not Always

Includes: FFC, JPS, PFF, PGF, PGX
by: Arbitrage Trader


Preferred stock duration is different from duration of conventional bonds.

Embedded call options make things complicated.

How to make sense of it all and position ourselves better in the rising interest rate environment.

I started my career as a trader of preferred stocks and I treasure highly my relationship with those instruments. Now, I have hugely expanded my universe of tradable securities, but none of those new securities could touch my heart the way preferred stocks can. For people who follow my posts regularly this statement probably comes as no surprise, but I thought I should share it anyway.

After the recent developments in the United States and the election of Donald Trump as a president, I thought it might be a good idea to see how the changed economic environment could affect my beloved preferred stocks. I have heard many people voice their concerns over the long duration of preferred stocks and how duration makes them sensitive to changing interest rates. But what do people mean when they talk about a duration of a perpetual security? Also, and this might be quite relevant for preferred stocks, what is the convexity of a preferred stock? Do those differ from duration and convexity of conventional fixed income securities? What is the place of embedded call options in the whole picture? How can we use these concepts to make better trading and investment decisions? In this article, I will try to find the answer to some of these questions and, hopefully, help you benefit from their understanding. Are you ready? Let's dive in.


First an Investopedia definition:

Duration is a measure of the sensitivity of the price - the value of principal - of a fixed-income investment to a change in interest rates. Duration is expressed as a number of years. Bond prices are said to have an inverse relationship with interest rates. Therefore, rising interest rates indicate bond prices are likely to fall, while declining interest rates indicate bond prices are likely to rise.

When people in general speak about duration, they either mean Macauley duration or modified duration. Macauley duration measures the weighted average term to maturity of a bond and is calculated using the following formula:

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Source: Investopedia

The modified duration, on the other hand, measures the price sensitivity (in % terms) of a bond to interest rate movements and is calculated using the following formula:

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Source: Investopedia

Now, those two formulas seem fairly understandable, but they are not applicable to securities that do not have a maturity date. In order to calculate Macaulay duration from the formula above, you need to have a maturity value, and in order to calculate modified duration, you need to be able to calculate a yield to maturity. So, what is the proper way to calculate a Macaulay duration for preferred stock then, when you do not have a stated maturity date?

To understand this, you should know that the duration is the first partial derivative to the price function with respect to the interest rates. I am not going to go into details about this, because it is unnecessary. The important thing is that we know the price function of preferred stocks and we also know how to take the first derivative of that function. When we do all the mathematical operations and when the dust finally settles, we have the following two equations for the Macaulay duration and modified duration of preferred stocks.

Where r is the current yield of the preferred stock.

Looks pretty neat, much nicer than the formulas above for conventional bonds. But what are the implications of the different duration formulas for preferred stocks?

First, let's see a price dynamic chart of two long-term bonds with different nominal yields, but similar maturity. The bonds in question are DTQ and DTZ, both of which are senior subordinated debentures issued by DTE Energy Co. (NYSE: DTE).

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Source: Author's spreadsheet

Not surprisingly, DTZ's price always stays above the price of DTQ due to its higher nominal yield.

Now, let's take a look at duration. From this point forward, I will be focusing my attention only on modified duration as it is a better indicator of a bond's sensitivity to changes in interest rates. If you are holding a portfolio of bonds, it's better to consider other metrics such as Macaulay duration or dollar duration.

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Source: Author's spreadsheet

Again, not surprisingly, DTZ has an overall lower sensitivity to changes in interest rates due to its higher nominal yield. But with the increase of interest rates, that advantage diminishes. Also, it is clearly visible that sensitivity to interest rates (in % terms) is level dependent and, generally speaking, bond prices are more sensitive to changes in interest rates when interest rates are lower.

Now, let's plot the price of a conventional fixed rate preferred stock at different interest rates and compare it to that of a bond. I have chosen to compare PRE-G to DTZ as both of them have similar credit ratings and the same nominal yield (6.50%).

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Source: Author's spreadsheet

Seems like the preferred stock performs better than the long-term bond when interest rates are lower and has a similar price to that of the bond when interest rates are higher. Be careful though - I am assuming that there is no call option embedded in the preferred stock and we all know that this is an unrealistic assumption as all preferred stocks have such an option. I will look into this issue later in this article.

Now, the comparison between modified durations:

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Source: Author's spreadsheet

As is visible from the chart, the interest rate sensitivity of the preferred stock is higher than that of the bond when interest rates are low and is pretty much the same at higher levels of interest rates.

Call options

Now, let's add some derivatives to the concoction. First, I want to say that in order to see exactly how call options affect the prices of preferred stocks and bonds, we need to agree on a valuation methodology for the embedded call option. There are a multitude of ways to come up with a value and some popular ones include the lattice model and the Black-Scholes model. I don't want to get into too much detail regarding those methods; I just want to see how they affect the price of bonds and preferred stocks. In the visual representation below, you can clearly see what the function of the bond price looks like when there is a call option embedded in the issue.

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Source: Harvard Extension School

The chart for the preferred stocks with an embedded call option is similar.

What does this imply for duration? Well, since duration measures the slope of the price function, the chart clearly shows that at lower levels of interest rates, duration is lower for the callable bond/preferred stock than it is for the straight bond/preferred stock. As interest rates rise, the call option becomes less and less relevant as it moves into out-of-money territory and the callable bond/preferred stock's price approximates that of the straight bond/preferred stock. Same goes for modified duration.

Also, bear in mind that the call option value is positively correlated with interest rate volatility, which is usually high when interest rates are low. That means that at lower interest rates, the duration of bond/preferred stocks is likely to be lower when interest rate volatility is higher.

How to trade it?

There are some indications that we would be seeing higher interest rates going forward, particularly in the U.S. where Trump's fiscal spending is likely to lead to higher real rates and higher inflation. Since we are currently operating in an extremely low interest rate environment, all fixed income securities are probably going to get hit hard by the rising rates. Preferred stocks are likely to take a bigger blow due to their generally higher duration. Also, preferred stocks with lower nominal yields, all else equal, will be even more severely affected. With regards to call options, they reduce preferred stocks' duration at lower levels of interest rates and are more likely to be exercised when interest rate volatility picks up, which is already starting to happen. The rising likelihood of the call option being exercised also reduces the duration of preferred stocks.

So, what preferreds I am looking at in this environment? I have my eye on currently callable preferred stocks that have high nominal yield, trade close to par and offer decent current yield and yield to call. Seems like I am looking for a unicorn, right? Maybe, but what about Aegon's (NYSE:AEG) 6.375% perpetual preferred stock (NYSE: AEH)? Look at some of the relevant information for the security:

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Source: Author's spreadsheet (YTC is calculated as if the callable stock is called for redemption in 1 month's time)

Hits all the checkboxes for me. I understand that when you are trading a preferred stock that is already callable, you are probably limiting your capital appreciation potential, but if what you are worried about is actually downside protection in case interest rates increase, maybe this is the best way to go.

One more thing - some of you might think that since preferred stocks have higher duration, they should be avoided altogether as an instrument in a rising rate environment, but I am a firm believer that if everyone is fleeing an asset class opportunities start to appear. Besides, if you start to get too worried about rising rates, you can always hedge your position. One way to do that is through fixed-for-floating swaps and another through shorting bond futures. And those are just two ways I can think of off the top of my head. I am sure there are plenty more.

Articles to come: Term preferred stocks; convexity in preferred stocks.


In this article, I wanted to show you how preferred stock duration differs from that of conventional bond duration. I also showed you how call options affect bond and preferred stock price dynamics and their respective modified durations. For people interested in investing or trading of preferred stocks, there is a way to do that while you also limit your exposure to interest rate risk and a good example of that is AEH.

In my next article, I will cover some issues related to convexity and will show you how the latter could affect positioning in preferred stocks.

As I mentioned in the beginning on the article, preferred stocks hold a special place in my heart, so I would appreciate any comments or discussions in the section below.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.