1.2.1   Dynamic versus Static Asset Allocation

• Dynamic asset allocation is an allocation that takes into account the link between optimal asset allocations across several periods. DAA thus takes a multi period view in regard to investment horizon.
• The approach recognizes that investment performance in one period has impact on the required rate of return and risk level acceptable for subsequent periods.
• For example, a manager will allow for charging parameters overtime using techniques such as ‘Monte Carlo Simulation’ thus incorporating expected changes to inputs as well as modeling unanticipated changes in macro-economic factors.
• On the other hand, static asset allocation ignores the link between optimal asset allocations across multi period investment horizon.
• A manager using static asset allocation might model necessary parameters at a point in time and then construct the long term portfolio using mean variance inputs.

Trade- Offs of Complexity and Cost

• Dynamic asset allocation approach is difficult (complex) and costly to implement.
• However, it’s preferred by investors with significant liabilities such as those with unpredictable timing and/or amounts (e.g. non-life insurance Cos) since it takes into account future expected cash outflows thus cost is appropriated.
• For investors with specific liabilities (e.g. DB Pension plans), asset allocation must be tailored to meet liabilities and to maximize the return, at the tolerable risk level.

1.2.2   Factors Affecting Asset Allocation Policy

1. Loss aversion – refers to tendency to prefer avoiding losses to acquiring equivalent gains. Loss aversion makes investors focus on gains and losses rather than risk and return as prescribed by modern portfolio theory. Loss aversion can lead an investor to take increasingly greater risk in an attempt to recover from a loss. This risk seeking behavior in turn can lead to highly concentrated or otherwise riskier portfolios.
2. Mental Accounting is the tendency for individuals to identify and immunize individual goals rather than use a diversified portfolio to meet all goals considered together (grouping economic outcomes into a number of non – interchangeable mental accounts)e.g. grouping by source of funds. This can be thought of as pyramiding approach. The investor focuses on immunizing the most important and highest goals with very low risk investments such as treasuries and high grade corporate bonds. Thereafter, lower (secondary) important goals are met using riskier investments. In this way, the investor moves in a step wise manner in identifying and immunizing goals of continually increasing importance.
3. Regret aversion – the tendency of past investment decisions – notably the regret associated with them – having irrational influence on future investment decisions. Regret is the feeling of disappointment or shame that investors feel from having to admit making a poor investment decision. Feeling of regret may be avoided by investor not actually realizing a loss holding out investment despite loss in value. Fear of regret can make investors to avoid taking actions that could lead to regret, such as realizing the loss by selling an investment. May lead to an investor holding a loser or a winner too long for fear of losing. Fear of regret can also result in investing only in investments considered comfortable and avoiding others. This may make the investor fail to hold investments that could improve the return/risk characteristics of the portfolio.

1.2.3   Return and Risk Objectives in Relation to Asset Allocation

• Return and risk objectives are determined in accordance with the investors constraints.

Return objectives

• To determine the rate of return for a portfolio, an investor combines distribution rate and future inflation rate.

Example

Portfolio has 100 units value, last year distribution – 5 units and 6% inflation.

Required: calculate required rate of return.

Solution:

Step1: calculate needed amount for distribution in coming period to account for inflation over the past year.

5 units *1.06 = 5.30 units

Step2: Calculate the distribution rate

5.30 units /100 units = 5.30%

Step3: Calculate rate of return needed to meet the distribution and maintain the real value of the portfolio after the effects of inflation in the future.

Additive:          5.30 + 6 = 11.3%

Note:

• Compounded and produces a higher return target.
• Compounded is preferred in multi-period settings and when there are path dependency issues (such as a distribution amount that increases with inflation and is likely to be associated with a lower portfolio market value).
• The difference in the methods is similar at lower rates of return.

Risk objectives

• The investors risk objective should be specified in relation to investors risk aversion.
• Investors can be categorized using a questionnaire with rating scheme on risk tolerance.

Risk measures

Then using quantitative relationship, determine the utility-adjusted return the investor will realize from a portfolio.

µ_p = Ȑ_p – 0.005(A) (ð ²_{p  )}

Where:

ð ²_p  = The portfolio variance

Example:

An investor has a required return before tax of 8%, risk aversion store of 7, and has 2 portfolio options:

B: Ȑ_B = 8.8%; ð = 10%

Required: Utility adjusted return

Solution:

U_B = Ȑ_{B –} – 0.005(A)( ð ²_B) = 8.8% – 0.005(7) (10%)²  = 5.30%

Alternatively, by using 0.5, the inputs must be entered on decimals

U_B = 0.088 – 0.5 (7)(0.10)²  = 0.0530 = 5.30%

Roy’s safety – first measure

• Measures downside risk such as shortfall risk, semi variable and target semi variance.
• Shortfall risk is the risk of exceeding a maximum acceptable money (dollar) loss.
• Semi variance is the bottom half of the variance (i.e. variance computed using only returns below the expected return)
• Target semi variance is the semi variance using same target minimum return such as zero
• Roy’s safety – first measure is stated as a ratio of excess return to risk.

RSF = (Ȑ_p  – RM_ar) / ð _p 

Where:

ð _p  = the portfolio standard deviation

Example:

Minimum acceptable return = 0 (Not lose any money)

Portfolio B: Ȑ_B = 8.8%; ð = 10%

Required: Determine preferred allocation (portfolio)

Solution:        

RSF_{B =}  (Ȑ_B – RM_ar)/ ð _p   = (8.8 – 0)/10 = 0.88

Preferred allocation = Allocation A (Higher excess return)