LDI based Private Wealth Management - Introduction

The concept of Liability Driven Investment (LDI) used for years in Institutional Portfolios, is slowly finding it use in Private Wealth Management. In this post, I will try my best to describe the benefits of splitting a savings portfolio up into a Liability Hedging Portfolio (LHP) and a Risky Portfolio.

Traditional Institutional Asset Management has up until recently been focusing around the search for the optimal portfolio with a clear focus on high expected returns. Such investments generally heavily tilted towards equities lost so much value during the downturn that many could no longer meet their obligations, i.e., making defined benefit pension payments or fund endowments. In many cases, the pension plan sponsor had to make up for the shortfall, sometimes with considerable financial consequences.

As a result of this disastrous experience, pension funds started to pay attention again to their primary obligations: future pension payments. This change led to renewed interest in money management approaches that explicitly take liabilities into account, an approach also called Asset-Liability Management (ALM).

While there are several, one technique known as cash-flow matching, involves ensuring a perfect static match between the cash flows from the portfolio of assets and the commitments in the liabilities. In a very simple way, this match can be made by holding a portfolio of inflation-indexed zero-coupon bonds that mature at the same time and notional, the pension liabilities. Although this technique is very simple (leaving aside the complexity relating to the uncertain life expectancy of the retiree, and the divergence between specific wage evolution and general inflation), it comes at the cost of very low average zero-coupon returns.

In an attempt to improve the profitability of the Assets, and thus to reduce the level of contributions needed, it is necessary to include Asset with a higher return, that may not be perfectly correlated with the liabilities. The objective therefore migrates to finding the best possible trade-off between the risk thereby taken on, and the excess return that the pension fund hopes to earn.

To implement such surplus optimization techniques, institutions build comprehensive models to capture the risk factors and their interrelations. The optimal portfolio can then be constructed, given some specified level of risk. While surplus optimization leads to higher expected returns and hence to lower contributions, than cash-flow matching the introduced risk exposure can be significant.

Liability Driven Investment (LDI) aim to manage such risk and usually involve a hedge of the duration and convexity risks via standard building blocks, while keeping some assets free for investing in higher yielding asset classes. In general, a fraction of the assets (known as the liability-matching portfolio) is allocated to risk management, while another fraction is allocated to performance generation. This technique may actually be seen as a combination of immunization strategies (for risk management) and standard asset management (for performance generation). It stands in sharp contrast to more traditional surplus optimization techniques, in which both objectives (liability risk management and performance generation) are pursued simultaneously in an attempt to achieve the portfolio with the highest possible relative risk/relative return ratio.

ALM in the context of Private Wealth Management


Given the recent increase in interest in LDI for institutional investment, as well as the available expertise, it is logical to ask whether these techniques could also be useful for the Private Wealth Management (PWM) industry. Within PWM clients are usually asked about their savings objectives, i.e., whether they want to set aside money for their retirement or perhaps for their children’s education. These are the client’s “liabilities”. The time horizon of the investment is also discussed. Next, sometimes using even more sophisticated methods, the client’s personal risk-return preferences are analysed to optimise his portfolio. Finally, to design the best possible investment plan, the contribution scheme must be taken into account, i.e., how much money the client is ready to set aside regularly.

The problem with current PWM practice is that these important factors are rarely sufficiently combined. So, although the banker’s advice might be beneficial from a risk perspective, the client’s liabilities are not adequately taken into account. Asset Liability Management, by contrast, makes it possible to merge the various needs for tailored solutions.

By explicitly including the individual liabilities in the asset allocation decision, it is possible to construct portfolios more efficient than those relying on standard asset management. The reason is that solutions that might be optimal from an asset management perspective are usually no longer efficient when the liabilities are taken into account.

ALM-based investment would provide protection from inflation risk superior to that provided by standard asset management. A similar case might be a wealthy retiree, who wishes to maintain a certain (real) standard of living but also to maximise her bequest to her children. Finally, wealthy families might be interested in making a large acquisition in the near future, such as buying property. ALM techniques allow for sound risk management of the related real-estate price risk of such an investment, as the following example will show.

An Example:
 Acquisition of a House


As an illustration of the ALM concept within private wealth management, consider the situation of a family who plans to purchase a house for their daughter once she has finished her studies. Suppose that she is expected to finish her studies five years from now, and that the current value of the projected house may be at €1,000,000. The family wants to set aside the required money through fixed annual contributions. The essential risk the family faces is hence unexpected changes in real estate prices. Given an appropriate model for the dynamics of property prices and reasonable parameter values, one may show that the expected price of the house in five years is at about €1,570,000, with a standard deviation of about €270,000.

The standard asset management approach in private wealth management would then be to find an investment solution that has a maturity of five years, with an expected value at maturity of €1,570,000. Usually, such an investment will consist of both bonds and stocks. If real estate prices rise at a slower pace than excepted (and hence the value of the portfolio exceeds the price of the apartment), the family is lucky and saves some money–if not, it must close the gap with another source of money.

The ALM approach instead directly takes the known liability of the investor, i.e., the house to be purchased in five years, into account when searching for the optimal saving strategy. Assuming that there exists an investment vehicle which is linked to real estate prices (such as REITS), one can decrease the variance of the difference between investment return and property prices (also called surplus volatility) significantly.

Because of the link between investment return and house prices, the family can reduce expected shortfalls at maturity. If real estate prices rise at a much higher rate than expected, the investment return will increase accordingly. On the other hand, if property prices slump, the investment will also yield lower (even negative) returns which is not a problem given the clear objective of the household. Although REITS do not hedge the investment risk perfectly, their positive correlation with the price of the envisaged acquisition can help to reduce the client’s risk exposure significantly.

Because of the trade-off between increased risk for an increase in expected returns, the client’s optimal portfolio should not only consist of REITS, but also other liability correlating Asset Classes.

The objective of the ALM technique is therefore to tailor the investment to the objectives of the family in a better way than through simple asset management approaches, which ignore the future purchase.

Since most of us don’t currently have enough Assets to finance future liabilities for example in the form of retirement savings, we construct pension savings plans. As such investments in a savings plan, is an active decision, to finance future liabilities, at the expense of current consumption, but of cause we would like contribute as little as possible. 

Savings Portfolios has historically constructed fairly static in the form of a increased allocation to fixed income at the expense of equities as investor got closer to retirement.

But Investing into different Asset should not be viewed at in isolation, but rather in the context of the future liabilities these Assets need to fund both of which are continuously affected by market performance and investor circumstances.

This is an important point, because whereas one investor may save for retirement in Spain and another in Florida, or investors have different tax regimes, time horizons or risk aversions, each has to face a unique Asset-Liability Management decision.

In such context, it may make sense to split the portfolio up into one part that seek to correlate with and immunize liabilities, and another more risky part that don’t need to correlate with liabilities, but should contribute to immunize liabilities while first and foremost lower the amount needed for frequent plan contributions.

The allocation to each part should be dynamic, since the relation between the Asset funding surplus vis-à-vis the future Liabilities, Inflation, Interest rates and investors risk aversion change over time.

The extend of immunization rests largely on striking a balance between (1) the value of assets versus liabilities, (2) the degree of immunization desired by the client in light of overall investment goals, and (3) market factors. A longer-term goal of increasing the degree of immunization, or even full immunization, rests on the notion that these issues are monitored and acted on over time. On the other hand, investors who have a considerable surplus of assets versus liabilities could implement a fully hedged ALM portfolio for a rather low cost (in terms of immunizing assets as a percentage of total assets).

A natural extension of ALM might consider the assets and liabilities of other balance-sheet items such as real estate, family-owned businesses, art collections, and potential legal liabilities, to name a few.

Another example:

The present value of an investor’s total future liabilities in the form of future spending, cash outflows, and capital requirements are modeled by discounting these liabilities over a suitable market-based yield curve (such as the AA-corporate yield curve).

The net present value corresponding to the horizon represents an investor’s total liabilities. Incrementally summed present values for each year in the horizon represent the nominal allocation to low-risk, immunizing assets for a chosen immunization period (in the case of a partially hedged approach).

The weighted-average timing of present-value cash flows represents the duration (or interest-rate sensitivity) of liabilities. Duration is measured both for total liabilities and for liabilities of a chosen immunization period. After the degree of immunization is established, a determination can be made regarding the basic allocation to low-risk immunizing assets (high-quality fixed income), and this information can be used as a constraint in the optimization process.

The primary goal of ALM is to reduce shortfall funding risks and allow assets in the portfolio to fund future liabilities. Hence, the degree of immunization implies the degree these risks are reduced. In this light, a trade-off often exists between the level of immunization and alpha potential. Making this determination is dependent on an investor’s level of wealth (assets versus liabilities), his or her goals, and his or her feelings regarding risks associated with future spending and market conditions. Because of these factors, the degree of immunization is determined on a situational basis. In subsequent rebalancing periods, the practitioner should look for opportunities to extend the ALM period as the value of assets versus liabilities improves and as market and client circumstances warrant it.

With the authors permission i reproduce a good example from the article "An Application of Asset-Liability Management for Financial Planners" by Jack Brown, CFA and Travis L. Jones, Ph.D. featured in the JFP.

John Doe has $1,000,000 in investable assets and a yearly spending need of $50,000 (see Table 1). This annual spending need will be met by withdrawing funds from the investment portfolio, and the amount will likely change with inflation or other unforeseen lifestyle changes. This withdrawal implies an initial spending rate of 5.0 percent. John is 65 years old with no medical problems and has an investment horizon of 30 years. The risk of assuming a shorter horizon relates to outliving his wealth. He has experienced a decline in portfolio assets as a result of recent investment performance. In response, he has made portfolio adjustments that reflect a lower level of investment risk (reducing overall stock exposure by 10–15 percent). Today, lingering feelings of a dangerous investment environment have led John to emphasize caution.

 511 Brown Table 1

John’s primary goal is having an investment portfolio that supports inflation-adjusted spending needs over time, with a secondary goal of wealth maximization over the investment horizon. Both John and his financial planner believe that interest rates will rise sometime over the next five years or so.

Table 1 shows John’s current asset allocation, which includes a 50 percent allocation to equities and a 50 percent allocation to fixed income (with a duration of four years). As noted in Table 1, long-term inflation is expected to be 2.5 percent per annum. In order to maintain inflation-adjusted wealth, an investment return would have to be approximately 7.5 percent, which includes the spending rate plus inflation.

Asset-Liability Management (ALM)

To determine the basic asset allocation between low-risk (immunizing) and riskier assets, we first identify John Doe’s liabilities over his entire horizon. For modeling liabilities, we apply discount rates (using the AA-rated corporate bond yield curve) to determine the present value of future portfolio outflows. International Accounting Standard 19 notes that the AA-rated corporate bond curve gives appropriate discount rates for pension liabilities; this rate is used here but is only a suggestion for practitioners. In Table 2, the first two columns represent each year in the horizon. Columns 3, 4, and 5 represent the future value of spending (portfolio outflows), the discount rate, and the present value for each yearly cash flow, while the sixth column illustrates the sum of the present value of spending or the dollar allocation required for each level of immunization given the number of years in the future. The final two columns present the percentage of the portfolio allocation required in immunizing assets and the aggregate duration required to immunize those liabilities for the respective periods in the future.

 511 Brown Table 2

If desired, Treasury Inflation Protected Securities (TIPS) could be used for a portion or all of the future spending offsets. TIPS offer insurance against unforeseen increases in inflation, albeit at a lower yield. For an analysis of using TIPS to secure income needs see Shankar (2009). To incorporate TIPS, adjustments to future values may be required, whereas real yields should be used for discount rates, which are yields on TIPS, for the relative offsetting periods.

For John Doe, the net present value of liabilities over his entire horizon is $1,055,201, and his portfolio value is $1,000,000. John has a balance-sheet deficit of $55,201; therefore a full hedge against liabilities is not possible with existing portfolio assets—the portfolio would be exhausted—thus this is not considered.

To determine the degree of immunization for John, we consider three scenarios: (1) the current allocation, (2) a partial immunization hedge covering 16 years of liabilities (the proposed solution), and (3) a partial immunization hedge of 25 years. See Table 3.

 511 Brown Table 3

Scenario 1. John Doe has a current (pre-existing) investment-grade fixed-income allocation of $500,000. This represents approximately 11 years’ worth of assets that could be considered as immunizing liabilities (see Table 2). However, the current allocation also presents a duration mismatch of approximately 1.7 years (current duration of 4.0 years versus 5.7 years at year 11 in Table 2). This represents an excess level of changes in assets versus liabilities due to interest rates. With a 50 percent allocation to equities, John has a significant degree of alpha exposure, which would be consistent with his secondary goal of wealth maximization. However, given John’s feelings about risk, we believe it is appropriate to place higher emphasis on his primary goal.

Scenario 2. Scenario 2 reflects our preferred immunization of 16 years (our proposed satisfactory solution) given John’s attitude toward risk, his primary goal of maintaining real retirement income, his secondary goal of wealth maximization, the low interest rate environment, and the overall deficit (total discounted liabilities exceed the investor’s portfolio value). This is a subjective period of immunization that represents a relatively low level of overall portfolio volatility; however, with an overall mix of assets that approximates the wealth maintenance return of 7.5 percent. A case could be made for 15 years or 17 years—the exact period of immunization is up to the financial planner in consultation with the client. A 16-year period, in this example, requires a 67.5 percent allocation ($675,094) to immunizing securities with a duration of 7.9 years. This scenario significantly reduces shortfall funding risk and helps secure future spending needs by increasing the fixed-income allocation by approximately 17.5 percent of portfolio assets and by extending the fixed-income duration from 4.0 years to 7.9 years. Immunizing 16 years’ worth of liabilities represents more than one-half of total liabilities in terms of time (16 of 30 years) and 64 percent of total liabilities ($675,094 of $1,055,201) in terms of value. The remaining 37.5 percent allocation to alpha-generating securities, equities in John Doe’s case, provides the opportunity to grow assets and allows time for interest rates to rise, which would allow for allocation to higher-yielding fixed income when rebalancing.

Scenario 3. Lastly, consider a 25-year immunization, an unsatisfactory scenario. Under this scenario, John has immunized 90 percent of portfolio liabilities ($941,913 of $1,055,201) with an 11.5-year duration for immunizing assets. While this scenario places a high focus on John’s primary goal, he has used 94 percent of his portfolio to achieve this immunization. Little room is provided for imperfections in the modeling process such as unexpected changes in inflation, changes in the horizon period, or surprises in John’s spending. Further, practically no adherence to John’s secondary goal exists, as a 6 percent allocation to equities provides little availability for real wealth enhancement. 

Perhaps it is most important to note that the degree of immunization is ultimately subjective, and as such, our alternative scenarios could be represented with different immunization periods. Determining a more precise degree of immunization could be achieved through various approaches. For example, a practitioner could compare implied allocations of various immunization scenarios with expected returns on an efficient frontier, such that the expected return exceeds the internal rate of return required to satisfy liabilities and approximates or exceeds the wealth maintenance return.

After a determination is made as to the degree of immunization, other asset-allocation methods, such as MVO or MCS, could be employed. These asset-allocation approaches would enhance efficiency by helping to direct assets among sub-asset classes or styles. In John Doe’s case, where we favor a partial immunization of 16 years, MVO would employ a minimum allocation of 67.5 percent to investment-grade fixed income with a duration of 7.9 years as a constraint in the model.

Longer-term rebalancing approaches in subsequent client meetings could focus on extending the immunization beyond the initial period and ultimately over the entire horizon. Subsequent meetings would take into account the client’s changing circumstances, changes in asset and liability values, market conditions, and other considerations as reflected in Table 3. Therefore, the time required to achieve full immunization might be several years. In the example, John’s primary goal could theoretically be achieved once he reaches a balance-sheet surplus of assets over the present value of liabilities. Regardless of a surplus, however, John’s secondary goal implies that significant exposure to alpha-generating securities (at least where real returns are expected to be positive) is warranted throughout his horizon.

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