**Asset Allocation**

It is well known that risk and return are closely related. Higher returns are generally accompanied by higher risk (or variability of returns, usually measured by standard deviation of returns). For example, CDs or GICs (up to federally insured amounts) issued by banks have lower but fixed returns than expected returns of bonds, but their returns will be variable with the interest rate environment (if not held to maturity). Furthermore, stocks are expected to have higher returns/variability than bonds. The question is then “how to build a diversified portfolio which gives you the maximum return at a given level of risk?”.

Groups of securities are called an asset class when they have similar risk and return characteristics. Asset class examples are stocks, bonds and commodities. One can also think of U.S. and foreign stocks as separate asset classes; same is true with bonds. To calculate the expected return and risk of a portfolio composed of many asset classes, one needs to know (or make projections/assumptions about) the future risk and return of and correlation between the various constituent asset classes, as well as their respective weights in the portfolio. The correlations are important as they measure the extent to which the returns of pairs of asset classes change relative to each other( Correlation of 1 and -1 indicate that they move perfectly together and perfectly opposite to each other, respectively; whereas correlation of 0 means the is no relationship between the movements of the two asset classes. Historically, correlations were low between stocks and bonds, domestic and foreign stocks, stocks/bonds and alternative investments (commodities, hedge funds, VC funds, etc). More recently, correlations between asset classes have increased, especially at time of financial or other crises. Furthermore, correlations between countries/and regions tended to be relatively lower than they are today. In today’s globalized world, some advocate replacing geographical diversification with industry diversification (a topic for a separate discussion)

For large individual portfolios and especially large pools of institutional money, there are very sophisticated analytical tools to construct portfolios. But for most individual investors various rules of thumb are often used to determine asset allocation. One of the most commonly quoted rules of thumb to determine stock-to-bond allocation is to use (100-age) as the percent of portfolio allocated to stocks (i.e. 25 and 75 year olds should be 75% and 25% in stocks, respectively). Others (like Ellis?) advocate that any assets you don’t expect to need for ten years or more should be in stocks. The single most important determinant in variability among portfolio returns is asset allocation, i.e. the weight of each asset class comprising the portfolio (Reference?). The portfolio performance can be measured against an appropriate return benchmark. Also, there are analytical measures to assess a portfolio’s effectiveness in taking risk to achieve the resulting return (e.g. Sharpe ratio) in a predictive way and/or after the fact. The asset allocation must insure that there are adequate cash reserves for near-term known requirements and possible contingencies for emergencies, in order to make it unnecessary to sell securities under duress during periods of significant price declines.

For a recently retired individual with slightly above average tolerance for risk, a 40% fixed income and 60% stocks would be a reasonable start. Then carve out a 5-10% cash allocation to cover expenses for 1-3 years. Geographical diversification is clearly important from a risk reduction perspective. But further justification for geographically diverse asset allocation would be for Canadians who spends a significant portion of time outside of the country, say in the U.S and wanted additional foreign diversification, to hedge against currency movements (a form of asset/liability matching). Such a portfolio (currency unhedged) would have suffered currency losses during the period of significant Canadian dollar appreciation (like 2002-2006), however it still had satisfactory performance and it does buy some peace of mind should the U.S. Canadian exchange rates would start moving in the opposite direction. In addition, to increase diversification 10% was allocated to alternative asset classes (not everybody will necessarily feel comfortable with a small dose of gold, commodities and/or hedge funds) These alternative asset classes historically have had low or negative correlation with stock and bonds.

I like to think of asset allocation in two dimensions: asset type (stock, bond, alternative, cash) and geographical. So from a perspective of two dimensional diversification, by asset class and geographical allocation, is shown below in percent:

**Risk Tolerance **

Risk tolerance is determined by your willingness and ability to take on risk.

Ability to take on risk is based on many factors, such as: age (younger has more recovery time and longer investment horizon), wealth (relative to needs), earning power (if necessary, can continue to work longer), short-term need for funds.

Willingness to take on risk is a function of your psychological makeup (usually assessed via a questionnaire such as the one used by Vanguard) and experience with risk (the type of past/current investments and the extent of their use or an entrepreneur approaching retirement may be more willing to take on risk than somebody who was employed throughout their whole life).

So, risk tolerance is somewhat subjective based on a composite constructed usually by the investment advisor, but together with Return Requirement, discussed next, will determine Asset Allocation. Often risk tolerance is expressed as “a loss no greater than x% per year” (say 95% of the time).

**Return requirement **

Return requirement is determined by available assets for retirement, years in retirement, expected inflation and desired income in retirement. Assuming no inflation, the return of the portfolio must meet your income needs. So for example, if you have $1,000,000 portfolio with a pre-tax income requirement of $75,000 and a pension of $25,000, then the portfolio must deliver a 5% return, i.e. (75,000-25,000)/1,000,000=0.05=5%. If however, there is an inflation of 3% (and assuming that the pension is indexed) then the portfolio must grow each year at an additional 3% to preserve its buying power. A simple way to think of it, is that if you do not wish (and/or do not need to) impinge on the buying power of your asset base, then each year you must earn what you take out plus the extra amount by which you need to increase the asset base to replenish what the inflation has eroded. Therefore, the required return is 5% 3%=8% nominal (or 5% real). The calculation is a little more complicated if the pension is not indexed or is partially indexed. The assumption here would also be that the 3% gain would be an unrealized capital gain, so no taxes would be due.

**Constraints **

There are constraints to consider in asset allocation and portfolio implementation. In the case of an individual/couple the most significant constraints relate to time horizon (e.g. time to retirement of a 25 year old vs. 50 year old, or a retired 60 year old vs. a 85 year old), liquidity (e.g. cash requirements ongoing expenses for next couple of years and major one-time expenses), tax considerations (e.g. interest vs. dividends vs. capital gains). A longer time horizon would generally mean a higher ability to assume risk and therefore a higher risk tolerance.

**Capital Market Expectations **

Capital market expectations are current views of long-term returns, volatility (standard deviation s of returns) and correlations among the various asset classes utilized in the portfolio. Historical data is available, but even than depends on what time frame is the raw data based on. Furthermore there are no assurances that the future will look like the past. Areas where future is more unlikely to look like the past is correlations between domestic and foreign markets; with the increased globalization and integration of markets, correlations have and likely will continue to increase relative to historical measures. Also, returns will likely be lower or higher than historically depending on whether you start your investments at a point of relative over or under valuation of the market. Historical data is a good place to start from and then adjust according to changes in expectations based on current environment.

Historically (Grinold and Kroner or West in Wurst.com slightly different period and results) between 1926-2001, inflation averaged 3.1% , 10 year U.S. government bonds returned 5.3% and S&P500 equity returns were 10.7%. Therefore, the 10 year government bonds returned about 2.2% over inflation, while the S&P500 equity returns were 5.4% (so called equity risk premium) above the 10-year government bonds. Cash typically returns 0.5-1.0% above inflation.

Looking at the asset allocation (assets and weights) example above and disregarding the geographical dimension, assume that you conclude that the capital market expectations are captured in the following table:

**Strategic Asset Allocation **

The Strategic Asset Allocation (SAA) is that allocation (i.e. asset weights in your portfolio) which meets your Return Requirement with the minimum risk and meeting your Risk Tolerance, within your constraints, for a given set of Capital Market Expectations. You recall that the calculated Return Requirement above is 8%. It is possible to calculate the overall portfolio return from the capital market expectations and weights.

The overall portfolio performance is:

Note that the return of 7.55% is below the required 8%. However the risk measure, the standard deviation, is 8.59% which is well below the risk of an all stock portfolio. So by diversifying away from an all stock portfolio, while we reduced risk significantly, we also ended up with a lower expected return. So we must still resolve the shortfall to required return. We could reduce our Required Return by 0.45% i.e. reduce our expenses by $4500 per year, or change asset allocation by increasing the stock allocation to about 0.60 while reducing the cash and bond allocations by 0.05 each, resulting in almost 8% (7.96%) return:

Note that the standard deviation, a principal measure of risk to be discussed below, has increased from 8.59% to 9.80%. The other interesting number is the Sharpe ratio, which a measure of the excess return over the risk-free rate (T-Bill) per unit of risk taken. It is a commonly used measure of portfolio’s risk adjusted return. Note that the Sharpe Ratio is essentially unchanged, so the excess risk is rewarded to the same level.

**Tactical Asset Allocation **

Tactical Asset Allocation (TAA) is the actual asset allocation implemented in the near-term, instead of the SAA, to reflect short-term views on the market. For example, if we believe that (medium to long term) bonds are overvalued (low effective yield) and cash returns are relatively higher as when interest rate curve is inverted), we may increase/decrease the allocation to cash/bonds. This results in a short-term deviation from the SAA, with the intent to return to it later. This may sound like market timing to you and you probably heard that it does not have a great reputation, and you may not want to pursue it as a standard practice. You may also have heard the old adage, what counts is time in the market, not timing the market.

**Measures of Risk (and Performance) **

Risk refers to the variability or volatility of returns. The most common measure of risk is standard deviation. Assuming that returns are normally distributed, it would mean that 90% and 98% of the time the return would fall within ( /-) 1.65 and 2.33 standard deviations, respectively. Another way of looking at risk is using ‘Value at Risk’. Value at Risk indicates that say 5% or 1% of the time the per day, month or year loss is greater than (Expected Return -1.65 or 2.33 times the standard deviation of return per day, month or year ).

A commonly used method of comparing portfolios/managers is to look at risk adjusted return. The Sharpe Ratio is a measure of the excess return over the risk-free rate per unit of risk (standard deviation) i.e. SR= (Expected Return – Risk Free Rate)/ Standard Deviation of Return.

For the two asset allocation examples above (0.5, 0.3, 0.1, 0.1) and (0.6, 0.25, 0.05, 0.1) we end up with Value at Risk figures of:

-5% and 1% of the time the loss will be greater than 6.5% and 12.5% (or $65,000 and $125,000 for a $1M portfolio), and

-5% and 1% of the time the loss will be greater than 8.2% and 14.9% (or $82,000 and $149,000 for a $1M portfolio)

**Monte Carlo Method**

Monte Carlo methods are used to answer questions that have no closed form solutions. The approach is based on using known or assumed statistical distributions associated with random input variables (e.g. Capital Market Expectations, inflation) to calculate a large number of output calculations (e.g. returns corresponding to an SAA) to infer the resulting statistical distribution of the output over the investor’s time horizon.

For example, Monte Carlo Tools can be used to evaluate effectiveness of various withdrawal schemes during retirement and the probability of exhausting the assets over a range of retirement intervals. In addition to accounting for cash flows (withdrawals), it is a means of factoring in the effects of inflation and taxes, which would be impossible in a closed analytical form.

To assume that returns associated with assets or inflation to be just the average or expected values of these random variables, would clearly lead to an incomplete/erroneous picture of the likely possible outcomes (e.g. a few years of low/negative returns early in retirement could result in running out of assets before death). The Monte Carlo method has become quite widely used in the past few years and many would consider analysis of retirement plan incomplete without its use.

An excellent example of the use of Monte Carlo tool is at** ****http://www.flexibleretirementplanner.com/**