Composite Returns: Portfolio Construction, Optimization, Simulation

An investment in a single fund has both market risk and manager risk. By constructing a portfolio of funds the manager risk can be minimized. Optimization allocates among the managers in the portfolio to maximize the return for the investor’s risk tolerance or minimize the risk for the investor’s desired return. Using a Monte Carlo simulation, the investor can predict the portfolio’s future returns or at least the likelihood of future returns.

Portfolio Construction

Whether a portfolio is constructed to provide exposure to the market or targeted exposure to a particular region or strategy investing in multiple funds will reduce the manager-specific risk. Figure 30 demonstrates the benefits of diversification using two asset classes, US Equities (S&P 500 Index) and Commodities (Barclays CTA Index), for the period January 1, 1995 through December 31, 1999.

Figure 30: Power of Diversification

US Equities and Commodities are not perfectly correlated. The lack of perfect correlation means that their gains and losses occur at different times. As a result, it’s less risky to be invested in a portfolio with exposure to both assets classes. How much exposure the investor should have to each asset class will be covered in the Optimization section.

This same principle holds true when investing in individual funds that are not perfectly correlated. The more funds in the portfolio the more the risk created by an individual manager is reduced. The risk that cannot be eliminated by diversification is the systematic risk or common sources of risk to all managers in the market, strategy, region and sector. At some point, there is a limit to the diversification benefit provided by adding an additional fund. There is a cost, both in terms of portfolio performance and financially, to invest in an additional fund that may exceed the diversification benefit.

To measure the benefits of a portfolio of funds a composite return series is created. The portfolio’s performance consists of the underlying funds’ performance, the allocations or weights to the underlying funds in the portfolio and the rebalancing schedule.

For one month the calculation of the portfolio performance is:

Portfolio Performance

Important factors in the calculation of portfolio performance are:

  • Allocation (weight) – Is the percentage of capital assigned to funds in the portfolio. Capital can be equally allocated across all funds in the portfolio, mandated by an investment policy or decided using optimization software to determine an ideal allocation.
  • Leverage – The investor can increase their position in an underlying fund by using leverage. For example, if the position is levered 2 to 1, we are taking a dollar of investor capital and borrowing another dollar to invest 2 dollars in the underlying fund, effectively doubling the position in the fund.
  • Rebalancing – When investing in private investments, the rebalancing schedule is typically never rebalanced due to the illiquid nature of the investments. Only a monthly rebalancing schedule will maintain the same starting allocations each month. The other rebalancing choices will allow the percent allocations to the underlying funds to change with the NAVs of the underlying funds until the portfolio is rebalanced. The common rebalancing schedules include:

a. Never – allocations are applied at the start date and the assets are allowed to grow. Never rebalance might be used with a buy and hold strategy, when invested in illiquid assets or while investing in funds with lockups which will not allow redemptions.

b. Annual – every 12 months the original allocations are applied. This rebalancing frequency might be used where the portfolio has target allocations that are maintained each year.

c. Semi Annual – every 6 months the portfolio returns to the original allocations.

d. Quarterly – every 3 months the portfolio returns to the original allocations.

e. Monthly – at the beginning of each month the portfolio resets to the original allocations. Monthly rebalancing is most commonly used when constructing a blended benchmark, e.g. 60 percent equities and 40 percent bonds.

f. Manual – any allocation can be given to any funds at any time in conjunction with other rebalancing schedules. Manual rebalancing represents a subscription in a new fund, additional subscription in a fund currently held in the portfolio and/or a partial or total redemption of an existing fund in the portfolio.

When the portfolio is rebalanced, in effect, for the funds that did well a portion of their gains are being sold and these gains are being invested in the funds that had losses to bring the portfolio back to the original allocations. Figure 31 isan example of quarterly rebalancing.

The portfolio starts January 1, 2011 with a capital balance of $10,000,000 equally allocated among four funds or $2,500,000 invested in each fund. On March 31, 2011 the funds’ allocations are no longer equal.

Fund A = $2,643,555.25

Fund B = $2,601,364.11

Fund C = $2,468,360.71

Fund D = $2,554,751.27

Summing the four positions gives a portfolio value $10,268,031.34. For an equally allocated portfolio starting April 1, 2011, each fund’s position value should be $2,567,007.84. Portions of Fund A and B’s gains are being sold and invested in Fund C and D in order to bring the portfolio back to its original equal allocations. At the end of each subsequent quarter the portfolio is once again rebalanced.

Figure 31: Quarterly Rebalancing, Selling the Winners & Buying the Losers
  • Lack of performance – When constructing a pro forma portfolio some funds may have inception dates after the desired inception date of the portfolio, thus lacking several months of data. The lack of performance can be addressed by reallocating to other investments in the portfolio or by using backfill.
  • Reallocating to other investments will proportionality redistribute the fund’s allocation to funds with performance untilthe fund does have performance.
  • Backfilling adds returns from another fund or index to the fund with the later inception date. The following common backfill approaches are:

a. Zero performance – equivalent to the percent of capital invested in the fund not earning a return for the months where the fund lacks returns.

b. Fixed Rate – equivalent to the percent of capital invested in the fund without performance earning the interest in a savings account.

c. Proxy Benchmark – for the fund without performance, the performance of the selected “benchmark” would be used until the fund in the portfolio has performance. For example, in Figure 32 the portfolio has a start date of January 2004 and Fund C has inception date of April 2004. For the first quarter of 2004 Fund C is been backfilled with the performance of the HFRI Index, the proxy benchmark in this example.

Figure 32: Using Backfill When There Is No Monthly Data

Investors who are required to select and monitor investment managers should develop a basic understanding of investment statistics. Quantitative tools can provide you with good insight that you can use in your qualitative interviews with managers and when monitoring your investments.