Financial Education

One approach to optimizing asset allocation is to use a mean-variance approach, which seeks allocations that maximize returns for a given level of volatility. These approaches select from various asset classes to combine them into a portfolio that maximizes risk-adjusted return. In an unconstrained mean-variance optimizer the only condition is that the asset class weights sum to one. In a sign-constrained optimizer, there can be no negative weights (short sales) assigned to an asset class.

Unconstrained Mean-Variance Optimization

In an unconstrained optimization, if the weights of any two minimum-variance portfolios are known, the weights of any other can be derived. For example, consider a world of three asset classes – A, B and C.

• The weights assigned to a minimum-variance portfolio X with an expected return of 11% are 70% A, 20% B and 10% C.
• The weights assigned to a minimum-variance portfolio Y with an expected return of 8% are 50% A, 25% B and 25% C.

To find the weights assigned to the minimum variance portfolio with expected return of 9% is found as:

• 9% = 11%(X) + 8%(Y)
• X = 0.67 and Y = 0.33

To find the weights of the individual assets:

• A = 0.67(0.7) + 0.33(0.5) = 0.634 = 63.4%
• B = 0.67(0.2) + 0.33(0.25) = 0.2165 = 21.65%
• C = 0.67(0.1) + 0.33(0.25) = 0.1495 = 14.95%
• 63.4% + 21.65% + 14.95% = 100%, so the equation checks

Sign Constrained Mean Variance Optimization

Given the constraint of no negative asset class weights, one finds that certain portfolios along the efficient frontier will be identified by holding identical sets of asset classes (in varying weights) and that the rate of change in asset weights moving from one portfolio to another is constant. At the intersections (where the set of asset classes change) are “corner portfolios.”

Much like the determination of a minimum-variance portfolio in an unconstrained mean-variance observation, if two adjacent corner portfolios are known the weights of any portfolio between the two can be computed as a weighted average of the two corner portfolios.

Pension accounting rules permit certain expense items to be smoothed into income. However, the required disclosures allow investors to adjust the income statement to reflect the true underlying economic cost related to pension plans. The economic cost should equal any change in the plan liability other than benefits paid or employer contributions.

Consider the following pension disclosures from KLA-Tencor’s 10K.

The pension obligation increases by 4,175, and benefits paid of $1,519 should be added back to that amount to determine the underlying economic change in obligation. 4,175 + 1,519 = 5,694.

The fair value of assets rose by $1,255. The contributions and benefit payments were a net $789 which should be deducted from this. Notice that in this case the benefits paid figure differs between the asset side and the liability side. It is possible some benefits were paid as a lump sum settlement. At any rate, the net change in assets was 1,255 – 789 = 466.

The net change in the economic liability, then, was 5,694 – 466 = 5,228. Contrast that with the reported pension expense.

The economic change in the value of the pension was $5,228, but the income statement showed an expense of just $2,280. An investor might want to adjust the income statement by adding $2,948 to pension expense, reducing operating income by the same amount. The effect on net income would be smaller due to the tax effects.

For KLA-Tencor, reported operating income was 589,868 in 2007. After this adjustment it would have been$586,920 – approximately half a percent lower. Earnings per share for the year would have been at least a penny lower.

Strategic asset allocation combines an investor’s objectives and constraints with long-term capital market expectations into an investment policy statement-permissible set of asset classes.

The purpose of strategic asset allocation is to satisfy the investor’s objectives and constraints, and the process leads to a set of portfolio weights known as the policy portfolio.

With regard to risk, investors expect compensation for any risk that cannot be diversified away (systematic risk.) Distinct asset classes have distinct risk exposures, and strategic asset allocation aligns the portfolio’s risk profile with the investor’s objectives to effectively control risk exposures. It also provides investors with a set of benchmarks outlining the appropriate long-term mix of assets and risk tolerance.

The Taylor rule is a guideline used to assess the central bank’s current stance and predict changes. It links the target short-term rate to inflation and GDP growth.

As a simple example, an equal-weighted rule could set the target rate as equal to a neutral rate, plus half the difference between forecast and target GDP growth rates, plus half the difference between the forecast and target inflation rates.

So, with a 3% neutral weight, 3% GDP growth target and 2% inflation target, if the forecast GDP growth were 2% and forecast inflation were 4%, the target short-term rate would be 3% + (0.5 X (2 – 3)) + (0.5 X (4 – 2)) = 3% – 0.5% + 1% = 3.5%.

Capital market expectations are an investor’s expectations regarding the risk and return prospects for different types of assets. They are considered a macro expectation (relating to the beta of asset classes) as opposed to a micro expectation (related to finding alpha within asset classes.)

Capital market expectations are a critical input to formulating a strategic asset allocation, because such an allocation can only be determined by estimating the risk and return characteristics of the various asset classes.

Foundations provide support for charitable activities, and although each foundation is unique there are many similarities when it comes to developing investment policy.

Risk Objective

Foundations tend to have high tolerance for risk because there is not a specific liability related to investment income. Although maintaining a given level of spending is desirable, it is not strictly necessary.

Return Objective

The primary objective is to maintain the real value of assets while spending at the desired or mandated rate. Many foundations prefer to maintain “intergenerational equity,” under which the inflation-adjusted (real) spending remains constant over time. If the foundation does not earn enough to cover spending plus inflation, then the real spending level will decline over time (at the expense of future beneficiaries.) By contrast, if the foundation earns far more than is needed to maintain real spending levels the current beneficiaries will be short-changed.

Constraints

Foundations need sufficient liquidity to provide for current spending. Often 5% of assets must be spent each year. Foundations have a perpetual time horizon and minimal tax concerns. There may be significant legal and regulatory requirements ranging from minimum spending levels, tax exemption status and compliance with the Uniform Management of Institutional Funds Act (UMIFA) or its non-US equivalent.  In addition, many foundations are funded with grants of stock in a single company – a unique circumstance that can reduce the ability to diversify investments.

Retirement plans generally come in one of two varieties: defined benefit (DB) or defined contribution (DC). In a defined benefit plan, the plan sponsor promises a specific future benefit, with no specific present obligation. In a defined contribution plan, the sponsor’s present contribution is specified but the future benefit is not. The distinction raises some important differences between the plans from both the empoyee’s and the employer’s perspective:

1. For the plan sponsor, DC plan obligations are fully met when the initial contribution is made. Sponsors bear a future liability in a DB plan.
2. Investment risk is borne by the sponsor of a DB plan, but by the participants in a DC plan.
3. Participants in a DB plan bear the risk of an early plan termination. There is no such risk to participants in a DC plan, because the participants own their own accounts.
4. DC plans offer portability to participants changing jobs.

A situational profile attempts to categorize an investor by stage of life and economic circumstance. Although doing so risks oversimplifying complex behavior, a situational profile can be a useful first step in determining the investor’s preferences and attitudes.

A situational profile typically includes a discussion of the sources of wealth, the measure of wealth and the stage of life.

Source of wealth can be important indicators of risk tolerance. Entrepreneurs may be comfortable with business risks but uncomfortable with risks they cannot control. Investors who inherited their wealth, by contrast, may be less experienced with risks and investing in general, and less confident in the ability to recover from setbacks.

Measure of wealth considers net worth. However, different investors may have different perceptions of how wealthy a given amount makes them. Investors who view their portfolios as being small are likely to tolerate less volatility than those who consider the portfolio to be large. The more the portfolio returns cover the investor’s spending needs, the more likely it is to be considered large.

Stage of life also influences attitudes toward investment risk and return.  In theory, the ability to assume risk diminishes with age, while the willingness to accept risk is driven more by cash flow (income less expenses.) Other factors may also have an influence, but investors are generally considered to pass through four life stages:

•  Foundation: investor establishes the base for wealth creation – skills, education, formation of business, etc.
  • Relatively young
  • Long time horizon
  • Above average risk tolerance
  • Need for liquidity may outweigh risk tolerance

  Accumulation: Rising income and wealth

  • Expenses rise during early accumulation phase due to marriage, children, home, etc
  • Expenses fall later in the stage as children leave home, mortgage is paid off
  • Income usually continues to rise, increasing ability to save
  • Increased wealth and still-long time horizon increase risk tolerance

  Maintenance stage (early retirement)

  • Need to maintain lifestyle and financial security
  • Wealth preservation becomes important
  • Shorter time horizon and lack of non-investment income reduces risk tolerance
  • Still need some risky assets to preserve purchasing power

  Distribution: Transferring wealth to others

  • Tax constraints become important
  • Planning for distributions can begin much earlier than distributions take place

The life stages are not necessarily linear. A career change could move the investor backward a stage, while an injury or illness could accelerate an investor’s entry to the maintenance stage.

IAS and US GAAP both require a statement of cash flows divided into operating, investing and financing sections. The two standards differ in the classification of certain items, particularly interest and dividend payments. The differences are summarized in the table below.

Arbitrageurs seek to exploit temporary market inefficiencies by buying a security they believe is underpriced and shorting a similar security they believe is overpriced. If the securities are not perfectly matched, the trade faces fundamental risks. But even if the securities are perfectly matched, the trade runs the risk that the inefficiency that produced it in the first place will continue or get worse.

For example, when Palm, Inc. shares were first spun out from 3Com investors were far more enthusiastic about Palm’s future than about 3Com’s. So much so, that Palm rose in value to the point that it was valued higher than 3Com – even though 3Com still owned most of the shares. Arbitrageurs sold Palm and bought 3Com knowing that when the remaining Palm shares were spun out they could replace the shares they had shorted and end up owning “free” 3Com shares.

However, the arbitrageurs (information traders) ran the risk that the investors who created the opportunity (noise traders) would continue to misprice the securities. If they continue to force Palm shares higher relative to 3Com, the arbitrageurs could be forced to cover their short positions early at a loss.