# Approaches for asset allocation

**1. The Mean – Variance Optimization (MVO) approach**

A significant drawback to generating an efficient frontier through traditional mean-variance optimization methods is the sensitivity of the frontier to changes in the inputs.

The input themselves (e.g., expected return, covariance) are estimates. Reliance on an efficient frontier developed through a traditional, single mean-variance optimization is questionable.

**2. Resampled Efficient Frontier (REF)**

– Michaud developed a simulation approach utilizing historical mean, variances, and covariances of asset classes, which combined with capital market forecasts, assumes they are fair representations of their expectations. His resampling technique is bases on a Monte Carlo simulation that draws from the distributions to develop a simulated efficient frontier.

– The simulation is run thousands of times, the efficient portfolio at each return level, and hence the resulting efficient frontier is the result of an averaging process.

– Rather than a single, sharp curve, the resampled efficient frontier is a blur. At each level of return is a simulated efficient portfolio at the center with a distribution of portfolios above and below it.

– The asset mix at any point on the resampled efficient frontier is an average of many portfolios thay might have been constructed to meet that return.

– By utilizing this resampled technique, a portfolio manager is able to judge the need for rebalancing.

**Advantages:**

– It utilizes an averaging process and generates an efficient frontier that is more stable than a traditional mean-variance efficient frontier. Small changes in the inputs variables result in only minor changes in the REF.

– Portfolios generated through this process tend to be better diversified.

– By comparing any asset mix of an existing portfolio to the range of asset mixed across the multiple portfolios on the REF that could have generated the required return, it is possible to see if the current mix is within the boundaries of what is acceptable.

**Disadvatages:**

Ther is no theoretical reasoning to support the contention that a portfolio constructed through resampling should be superior relative to another constructed through traditional mean-variance analysis.

In addition, like MVO, the inputs are often based on historical data that could lack current relativance.

**3. Black – Litteman**

With the same motivation as Michaud (resampling), Black Litterman developed two modes for dealing with the problem associated with estimation error, especially expected return:

– The unconstrained Black-Littlerman model (UBL)

– The Black-Litterman model (BL)

The assigned reading focuses primarily on BL (i.e., constrained for no short selling)

**The Unconstrained Black-Litterman Model (UBL)** starts with the weights of asset classes from a global index.

Applying a Bayesian process, the manager increases or decreases the weights based upon her views of expected asset class returns and the strengths of those views of expected asset class returns and the strenghs of those views with no constraint against short sales (negative weights are allowed).

The UBL is intuitive in that the manager starts with market weightings and directly increases or decreases those weights based on the manager’s opinion of what will outperform or underperform.

If the manager has a strong opinion domestic equity will underperform, the manager can shift significant assets out of domestic equity to specific asset class expected to outperform or broadly across all other classes if the manager has no specific views on what will outperform.

UBL does not define how to make these adjustment to weights, but in practice, most managers select relatively diversified portfolios without negative weights.

**The Black-Litterman (constrained) model (BL)** allows no negative asset weights, also produces well-diversified portfolios that incorporated the manager;s views on asset class returns, and is a more defined process.

It is a rigorous mathematical process starting with reverse optimization. BL can be used to both calculate the market’s consensus expectations of returns by asset class and then construct an MVO portfolio adjusted for the manager’s views of those returns. The BL requires several step:

– Select a relevant, global market index. Input the market weights for the asset classes in that index and a covariance matrix for those classes.

– Use reverse optimization to back solve for the implied, expected returns of those asset classes. Having started with a market index and the market weightings, these will be consensus returns expectations.

– The manager then reviews the implied returns and expresses any opinion regarding the returns and the strength of those opinions.

– The manager then resets any implied returns up or down to reflect the manager’s opinion and conviction level.

– A new MVO is run using the adjusted returns where the manager had an opinion and the market consensus return where the manager has no opinion. The new MVO produces the recommended asset mix.

Unlike UBL, the manager’s opinions and level of conviction are incorporated. But BL then uses MVO to also factor in asset volatility and correlations in a disciplined process to find the optimal mix. BL tends to be less sensitive to changes in inputs and less likely to produce the under diversification common in traditional MVO.

**4. Monte Carlo Simulation (MCS)**

– MCS is a statistical modeling tool often used to complement MVO or other asset allocation tools. For example a manager could begin by selecting several optimal portfolio using MVO that have acceptable risk and return for the cliendt and then use MCS to generate multiple simulated paths displaying how these portfolio would perform over time. The MCS can consider path dependency effects on the portfolio, such as a constant nominal or real amount of funds withdrawn periodically or taxes paid on the returns.

The MCS paths could be ranked in order of value to facilitate answering such questions as: will the portfolio be exhausted? When? How bad or good could it be?

**5. Surplus Asset Liability Management**

– ALM approach searches for the set of allocation, which maximize the different (the surplus) between assets and liabilities at each level of risk (much like the efficient frontier represents the maximum return at each level of risk.

– The vertical axis is the value of the expected surplus, and the horizontal axis represents the associated risk, measured by standard deviation of surplus.

– As with any efficient frontier, there is a minimum-variance portfolio, which in this case is the minimum variability of surplus. With the lowest risk, it also generate the minimum expected surplus.

– Beta policy decision: The choice of any portfolio on the frontier is a client and manager decision, they accept more and more risk as they move out on the frontier. Because it is a riskier decision than selecting the minimum surplus variance portfolio (MSVP) it could be called a beta policy decision.

– The ALM efficient frontier could also be presented in terms of the funding ratio ( i.e., the value of plan assets devided by the value of plan liabilities). In that case, the ration is presented along the vertical axis, as either a percentage or a ratio, and risk is plotted along the horizontal axis. Other than the way the vertical axis is labeled, the analysis is the same.

– As with other optimization procedures, ALM requires estimations of all associated mean-variance parameters and thus suffers from the same estimation biases. Of course, this now also includes estimating the liabilities as well. To help avoid these inherent limitations of MVO, the manager can utilize a resampling technique or the Black- Littleman approach for ALM. Monte Caro simulation could then be added as a complement to examine path dependency and gain insight to the behavior of the surplus over time.

**6. Experience – based Techniques (EBT)**

EBT is just the process of elimination. The EBT approach is more typically used with individuals who lack the background to understand the more mathematical approaches. This is less of an issue than it might appear because the experience-based rules of the process of elimination are in fact generally well supported by the more mathematically based approaches.

**Common EBT rules including the following:**

– A 60/40 mix of equity and fixed income is a good starting point for the average risk investor. More aggressive (less aggressive) investors should increase (decrease) the equity allocation and make the corresponding adjust the fixed income allocation. A longer time horizon is generally consistent with more equity.

– 100 – investor’s age is sometimes used as the starting equity allocation.