Abstract:

This publication starts with a risk-free 2-year strategy that provides proportional exposure utilizing government treasury bills and 2-year call options. After that we discuss strategies that may increase risk with improved returns. The alternative risks may be financial or time based depending on the strategy. Finally, we discuss how this strategy could be tailored to any individual investor.

*Disclaimer: This is a thought experiment and a market strategy. Whether it is right for your portfolio is your choice and if you have a financial advisor then maybe it is best if they read this. Depending on your bank, fees margin and interest on options may change.

Introduction

Individual investors like the yields of the market but typically do not wish to lose money. Because of this, many of these investors seek yield via Savings Accounts, CDs, or Bonds. Other life insurance type products exist where they guarantee no risk but gains are capped.

The below strategy shows how one can proportionally replicate the market performance using a S&P500 market ETF (SPY) with no downside risk. Then we look at alternative risks for increased gains. For example, there can be time-risk incurred while waiting for a bond to expire, however, the increase in return is that these instances the strategy will outperform the market versus an account holding only SPY. 

A bond is a timed debt instrument with a maturity date and value that is backed by an organization such as government and corporate entities.  The risk in a bond lies within the issuer’s ability to pay the face value back at maturity.

Typically, a bond is purchased for less than $100 and the face value or value at maturity is $100.  So, a 2% 1-year bond would roughly cost $98, and over the course of a year approach the value $100.

An option is an instrument designed to allow you to purchase or sell an asset. For example, a farmer, to fix the price of corn, may purchase an option to sell corn at current market rates to have price stability through the grow season. The option comes with a fee to the bank based on the underlying asset and time period of the option.

An option to purchase SPY, the largest S&P 500 ETF, 2-years into the future for roughly the price it is today is called a “2-year at the money call” on the SPY.

The strike price of an option is the locked in price of the asset. An at the money call has a strike price near the price of SPY. If the price of SPY exceeds the strike price, the option is said to be “in the money.” If the price of SPY is lower than the strike price, the option is said to be “out of the money.”

Introduction & Analysis

For the purposes of simplicity and this paper, we will be writing about 2-year bonds and 2-year call options. That is the maturity date on the bonds are roughly 2-years from today, and the option to purchase has a strike date roughly 2-years into the future.

Let’s name the price to purchase the option, OP and the strike price, SP. 

OP/SP is the percentage or ratio of the option fee. Therefore, if one wanted to determine how much money is required to purchase $D of the underlying asset, that would be D*(OP/SP) = OD. D is really important to our analysis, because it is the number of dollars of the underlying asset we are controlling. Taking it back to the farmer example, $D is the number of dollars of corn the farmer is trying to sell. In our case, $D is the number of dollars we are attempting to invest into SPY. 

Example: On the week of Dec 15, for a 2-year call option on SPY,  OP/SP was roughly (80/590)=0.135 or 13.5%. That means to purchase a 2-year at the money call option to acquire $1,000,000 of SPY would cost 1000000*0.135=$135,000. 

Similarly, if we have an amount of money used to purchase the option, $OD, then OD*(SP/OP) = D. Again, $D is the amount of dollars invested in the underlying asset. This calculation is a useful tool because when one purchases the bond, they know OD, but understanding the performance depends on $D. 

At option expiration, if the price of the underlying asset is less than the strike price of the option, it is worthless. That is the risk associated with purchasing an option. Having said that, we are purchasing the option with the “interest” from the bond and so, essentially the bank fee to hold the option is “free.”

Now consider X to be the number of dollars in a portfolio wanting market exposure. Suppose, instead of placing X into the market, we instead purchase a U.S. Treasury bill with a maturity 2-years into the future with a face value of X.

The bond’s purchase price BP < X. So, the remainder, X-BP we will call IN for interest but essentially the strategy is that OD = IN. This is also the money we will earn as interest over the next 2-years via the bond. 

Remember, the value of the bond at the end of the 2-year term is the face value or X and so, unless the United States Government does not pay the bond, the account is GUARANTEED to not lose any money.

We want market exposure at a significant level, and so we take IN to purchase as much SPY options as we can. Then amount of dollars of the underlying asset, SPY, we are have the option to purchase is D, or  (X-BP)*(SP/OP) = D.

Because over the next two years, the performance of the option will match the performance of the underlying asset to the upside of SP on $D. The portfolio with bond and option will also match the performance of the underlying asset to the upside at a ratio of D/X because we are matching the performance on D dollars. The bank fee for the option is “paid” by the interest of the bond IN and so no money was risked at the end of the 2-year period.

The value of the portfolio at the end of the 2-years is:

X+(performance of underlying asset or 0 )

Let’s take a concrete example with the SPY.  If one had $1,000,000 and purchased a 4% bond priced roughly at $92, they would have $80,000 to place into a 2-year spy call option. $80,000/0.135=$592,592.59 of underlying SPY shares.

Therefore, the rate of return of the portfolio would return roughly 59.2% the rate of return of SPY. If spy rises 10% over the next 2-years, the portfolio would have increased 5.92%.

If SPY after 2-years decreases or closes at strike price, then the portfolio is at X, and so no money is lost or risked.  

If a “black-swan” event occurs and the price of SPY is cut in half, most of the money is in the bond, one could purchase the event by selling the bond and purchasing either SPY options or SPY directly. 

The strategy is essentially without risk, though an astute reader would say that there is opportunity cost versus potential other investments. For this thought experiment, the idea was capital preservation and in the cases where this strategy would carry 0 interest for two years, those investing in a vanilla SPY strategy would be losing money, and so therefore, in the case where we lose the opportunity, we still outperform the market over the same period of time.

This particular strategy is risk free because the interest paid the entirety of the option cost. Because the market is up more years than it is not up and when $D < $X we are underperforming a vanilla SPY purchase for $X that day.

We have to remind the reader now again of the risk of purchasing an option.  The risk is if for some reason on expiration date the S&P 500 closes below the strike price of the option, that option is not worth anything. 

That could look like you are up 40% right into expiration day and then there is a crash that day and the market closes below the price that day.  Averaging in and out of options as an advisor would do for stocks is recommended which means purchasing and selling positions in smaller chunks. 

That could also mean the market is on a two year flat or downtrend.

Where is parity with the market?

The next questions that arise is what happens if we are willing to take small amounts of risk.  One way to do this would be to purchase “riskier” bonds with higher interest rates.

Let r be the interest rate we are able to obtain through a “bond portfolio,” a set of bonds at different interest rates. As we increase r, we can create a higher D because it increases IN. 

OP/SP was a 2-year percentage while r is the measurement for one year. Therefore, OP/(2*SP) = r is parity with underlying asset. That is when D=X or the value of the underlying SPY purchase matches the account value. When this happens, the portfolio will behave on the upside as though it is $X of SPY and not carry the downside risk. If the money in the bond is held to maturity, the account ends back at $X.

Parity to market upside returns for reduced downside risk.

If a market participant is willing to accept loss, the strategy of purchasing the call option caps the losses at the OP/SP rate if purchased so as to have the option to purchase $X of underlying asset.

So, purchasing $1,000,000 worth of SPY via purchasing the option limits the downside to the 13.5% paid for the option. One could offset this by placing X-OD fully into bonds reducing the downside risk incurred by purchasing the option by the interest rate over 2 years. In the example, the downside risk is reduced to 5.5%.  

Market Outperformance and Increasing Returns

It is possible that D > X when r > (OP)/(2*SP) or when IN > D > X. If that occurred, we create market outperformance for the portfolio through this reduced risk option/bond strategy. These strategies have zero risk if bonds are held to maturity, though, if the interest is lost in a situation where the option expires worthless, one may incur opportunity cost against the market until the bond matures.

Because the option purchases can match a stock portfolio, with long-term options, one could recreate their portfolio at no risk within IN. Therefore, any market outperformance strategy could also increase returns.

Parity for a Fixed Reduction in ROI.

When purchasing an option, one may purchase a call option out of the money for reduced price. Therefore, another strategy would involve finding parity on the price list for the option out of the money. Let’s say MP or market price represents the price of the underlying asset, or in our example SPY.

When MP < SP, when the option is purchased the purchaser will not participate in the first SP - MP gain in underlying value. Therefore, if using this strategy, the first (SP-MP)/MP percentage gain is not incurred at the end of the 2-year period, but everything after that is incurred. Also, if that minimum percentage gain is not reached, then the option expires worthless. 

As an example, if the SPY gains 40% in 2 years from MP, and SP is 10% higher than MP, the gain incurred by the purchaser of this option is 30%. Having said that, this is not a proportional reduction in gains, this is a fixed reduction in gains allowing us to further improve performance by choice of option.

Parity with X on the bond interest is then reached when (OP/2*SP) = r or 2*r*SP = OP.

If OP < 2*r*SP, it provides an opportunity to increase D and have the underlying purchase value be worth more than X in underlying asset. In other words, in our 1 million dollar portfolio, we could purchase the option to purchase 1.4 million dollars worth of SPY because the price of the option is reduced and the strike price is higher. 

Bond Term Variations

Another strategy that can allow us to increase IN is increasing the bond term to a longer period. That is because 5-year bond has a higher interest rate and its BP contains several years more interest in discount over the 2-year bond. The added risk is that in the unlikely event that the 2-year option expire worthless, the purchaser may be required to hold the bond to term with no market exposure to recover the initial investment. Because we are using options instead of purchasing stocks directly, there is a challenge in that we do not have the ownership of the underlying shares.

It appears five-year treasury with a five year duration offering a yield of 4.5% could be purchased for about $80, allowing an 80/20 bond/option split.  In our X = $1M portfolio that allows us an option over purchase of $200k causing D to be 200000/0.135=1481481.481 — a 48% overexposure to the market versus X allowing for a 48% outperformance of the vanilla SPY portfolio over the 2 year period with a high bond value for protection. For this strategy, there is a time-value risk incurred if for some reason the underlying options expire worthless in 2-years in that one may need to wait up to three years for their account to return to its original value. Selling the bond at that time would forfeit that interest, and depending on rates at the time of the sale, the loss would be approximately 3r *X.

At the same time, a 3-year bond at 4-5% interest rates gives the purchaser parity with the market. The downside risk is the option expiring worthless in 2 years. At that point in time the bond could be sold at the loss of one year interest and market variation or held to reach full value in 1 year. That improves the risk over purchasing the option to reach par with the S&P500 and at a higher rate may offer improved performance against the S&P.

Portfolio Risk Mitigation for Individuals

Simple risk mitigation strategies such as creating a 5-year bond ladders could help mitigate this risk by allowing multiple new natural purchase points into the market as bonds are repurchased. It also allows investors to “dollar cost average” should the market be lower 1 year into the trade or should they wish to reduce market position for a new 2-year position. They always have the option to “go all in” by selling the bonds and purchasing the market if there is a steep downturn thereby making this an inherently better option over the vanilla SPY ETF account which would lose that value.

Similar risk mitigation could occur within the S&P option purchases allowing for “averaging down” rather than going “all in” immediately on the market. This mitigates the risk of the one option expiring worthless. These strategies are all extremely low risk because the majority of the money (over 50%) is placed into bonds, and the interest equals the bank fees on the options. 

Combining strategies to increase r and IN while also introducing strategies to reduce market risk can help mitigate a risk averse client. Active management can allow for position trimmings and rebalancing the bond/option ratio as the portfolio value grows.

Finally, these strategies could be fully customized to most investors as they are able to fully replicate an equity or bond account via the strategy using options for two year periods by utilizing the bond’s interest. Their ability to get the cumulative $D to equal $X may be challenged by the option pricing on individual names which can run at a higher OP/SP.

Conclusion:

The real driver that makes the strategy work is that the options allow us to drive up the market exposure for a time period. Utilizing the interest of bonds to mitigate cost can provide proportioned market exposure including overexposure. Having said that, a bond/stock split, while offering a lower yield, have a higher guaranteed yield because he theoretical value of SPY will not be zero.  

A follow up study will be done on how does this strategy compare to a bond/stock portfolio and what the theoretical results are of using all three together.

‍