MORAM Portfolio Immunisation
Education

Educational: Portfolio Immunization

Suppose you are managing the fixed-income portfolio of a commercial company and have to face a known large outflow in the upcoming years with a known amount but uncertain timing. How would you construct your portfolio to face this liability so that the fluctuation in interest rates doesn’t affect the value of the portfolio against the liability? 

LDI is the strategy to cover future obligations with invested assets (usually in fixed-income securities) and is mainly used by institutional investors like pensions or insurance funds. However, this may also be relevant for commercial corporations seeking the coverage of debt repayments or defined-benefit pension plans, but also for individuals (supplement for the public pension, or a downpayment for an apartment, to say some examples).

One of the most common LDI strategies is immunization which minimizes the variance between the return of assets and liabilities. It may be seen as a special case of interest rate hedging. The goal of immunization is to protect investors against fluctuations in interest rates that may affect the value of their bond portfolio. We will see through the examples how to structure a fixed-income portfolio protected against interest rate changes through duration matching. 

If we took the simplest example, let’s say a one-time downpayment for an apartment in two years, the maths and the portfolio construction would be simple: Invest in a high-quality (assumption: no-default risk) zero-coupon bond security for two years. For a $50,000 downpayment and a YTM of 4%, we would have to invest  ($50,000(1+0.04)2)=$46,227.81As we are holding the security to maturity and the durations are the same, we have no price risk (ultimately the bond will be brought at par), and as we do not receive any coupon, we do not face reinvestment risk either. So, the interest rate volatility is ultimately irrelevant to us as buy-and-hold investors. 

Unfortunately, the reality is a bit more complex. Despite being about three times larger than the equity market, zero-coupon bonds are not as common as coupon-paying securities. Moreover, we would have to find a bond with the same duration of the liability.

This is why, to immunize our portfolio we will have to construct a diversified bond portfolio with the following assumptions/ characteristics:

  1. The market value of the assets is equal to or higher than the present value of the liability. As most of our readers are equity investors, you must be thinking: Then, why doesn’t the company repurchase the bond if they have enough funds? The answer is simple, bonds are not as liquid as equity, and many fixed-income investments intend to hold to maturity their securities. If the company intended to buy back the bonds, they would have to pay a premium and can synthetically do the same building a bond portfolio. 

  2. The Modified Duration is equal to the liabilities maturity date. The idea of doing so is that the price and reinvestment risk cancel out. * We have already covered the basics of fixed income in other posts, in case you feel you are missing something, you can always take a look in the portfolio management section.

  3. It minimizes the portfolio convexity statistic. The biggest risk of the immunization strategy is the non-parallel shift of interest rates. To minimize this risk, we need to reduce the dispersion of the cash flows thus minimizing the convexity of the portfolio.  To do so, we need to construct a laddered portfolio. 

Let’s imagine you are the investment manager of a manufacturing company in Germany. Three years ago, your company decided to invest in a huge factory in the US, and to do so, the firm issued a 10-year zero-coupon putable bond.

Note: if we wanted to match the outflows of the liability with the inflows of the fixed-income portfolio, we should use a cash flow matching strategy. However, our objective is not this one but to be ready to repay the investors in case they use their put option.  This is why they want to protect themselves against the fluctuations in interest rates. 

Three years after buying the facilities and borrowing the loan, the company decided to shut down its operations in the US and sold the factory for $100MM in cash. As of today, 31st December 2023, the bond is trading at par with the following figures:

MORAM - Portfolio Immunisation

As we said in the beginning, this is a liability-driven strategy, thus, once the liability is quantified, we can build our fixed-income portfolio. Remember: Our objective is to match the duration of the liability with a portfolio of bond securities so that we have no impact from a change in the interest rates. As our liability was in USD, we will construct our portfolio by combining Treasury bonds of different maturities. You can find the current price and YTM of these and many more securities in Bloomberg.

Treasure bills

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