Let’s talk about asset liability hedging with bonds! It’s a very well practiced strategy for large institutions and pension funds albeit they also integrate stock portfolios into the mix. Typically the industry will use a combination of risk-on and risk-off allocations. If you attempt to have one set of allocations behave in a multitude of manners you’re likely to underperform all the strategy specific goals.

Firstly, let’s say your business or fund has 7 million dollars in total due in the next 4.5 years. However, the payment amounts and due dates vary. How do you calculate this into an aggregate sum to do math conveniently?

Calculating Present Value of Liabilities

A sum of money now is often less than in the future. We can apply this principle to liabilities.
The concept is that if we invest our money in a bond that pays 3% interest annually our initial sum required to pay off the total debt is less than the sum.

Mathematically this looks like…

… where B(t) relates to the rate of return of the bond and PV(L) relates to the present value of the liabilities.
If the math is intimidating feel free to Google “Present Value Calculator” and apply the concepts in an assisted fashion.

Liabilities

1.0M – 3.0Y
1.5M – 3.5Y
2.0M – 4.0Y
2.5M – 4.5Y

While these liabilities total $7,000,000 since they are due in the future with different payouts one would only need…
$6,233,320.32 to afford the payments. This is due to the time value of money given by the market.

This concept may appear obvious to many but it is surprising how few account for the actual present value of liabilities and instead use the full amount.

Calculating Funding Ratio

Funding Ratio’s are commonly used in pension funds and financial situations when future disbursements or payments are known.

The math on this is a simple ratio of …
assets / present value of liabilities

As an example to illustrate how important the interest rate is on the bond, let’s say we only have $5,000,000 and have 3% and 2% rate scenarios.
5M at 3% puts our funding ratio at 80.21%
5M at 2% puts our funding ratio at 77.20%

Hopefully this has been a simple concept to understand and one you can keep in mind for future DIY finance.

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Fischer Black and Myron Scholes first met at the Massachusetts Institute of Technology (MIT) and started a working partnership that would last for 25 years. They are well known for their pinnacle achievement — the Black-Scholes Option Pricing model — which revolutionized investing and led to a Nobel Prize. However, there are many contributions that the the two made individually to the world of investing. Constant Proportion Portfolio Insurance is one of those contributions and was introduced 15 years after their original Option Pricing model.

Black and Jones introduced Constant Proportion Portfolio Insurance (CPPI) in 1987.

The strategy involves de-risking a portfolio as a predetermined cushion has been breached. Once the safety cushion has been breached the portfolio is reallocated with increasing risk free assets. The dynamic nature of the strategy responds well to market conditions that do not exceed the cushion per monthly period. An investor does not need to use options to implement the strategy.

You can download the original four page paper published in 1987 here: Black_Jones_Simplifying_Portfolio_Insurance_1987

Presented in a visual manner the strategy looks like this…

The dynamic allocation between risky and riskfree assets allows for the construction of convex payoffs similar to options without the use of option hedging. This makes the strategy more applicable to a wider range of account types that do not allow the use of derivative hedging.

Let’s look at a real world practical example on implementing CPPI…

Cushion (C) = $20,000 (P X F)
Multiple (M) = 3
Total Portfolio (P) = $100,000
Wealth Preservation Floor (F) = 80%


Initial Investment in Risky Asset = M x C
Initial Investment in Risky Asset = 3 x ($100,000 x 0.80)
Initial Investment in Risky Asset = $60,000

Initial Investment in Riskfree Asset = $40,000


The risk in CPPI trading is known as gap risk.

Gap risk occurs when you have breached below your trading cushion before reallocating your portfolio. Gap risk will occur if the loss on the risky asset is higher than 1/M. In the above example that would equate to 33.33%. It is recommended that your reallocation frequency takes into account the potential volatility over the period duration between reallocation.

Reallocation process after drawdown…

Let’s assume a 10% drawdown and reallocate the CPPI strategy.

Updated Cushion (C) = $10,000


Reallocation in Risky Asset = M x Updated C
Reallocation in Risky Asset = 3 x $10,000
Reallocation in Risky Asset = $30,000

Reallocation in Riskfree Asset = $60,000


CPPI is especially useful for mitigating bear markets and reinvesting at bottoms for outsized returns.

Good luck implementing CPPI in your investing strategy!

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