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Domestic-Currency Return formula

Rdc = (1 + Rfc)(1 + Rfx) – 1

Rfc = Return as measured in a foreign currency

Rfx = Return due to foreign exchange movements

Rfx is not always %ΔSp/b ie not always the % change in the spot rate


6 keys to effective investment governance

  1. Clearly articulate long and short-term investment objectives
  2. Careful allocation of decision rights and responsibilities
  3. Developing and approving investment policy statement to govern day-to-day operations
  4. Specific process for developing and approving strategic asset allocation
  5. A reporting framework to monitor progress towards the agreed-upon goals and objectives
  6. Periodic governance audits

3 possible reasons rebalancing earns a positive return

  1. diversification return
  2. return for being short volatility
  3. supplying liquidity to the market

Surplus Optimization formula


E(Rs,m) is expected surplus return for asset mix m defined as:

(Change in Asset Value – Change in Liability Value) / Initial Asset Value

6 Criticisms of Mean-Variance Optimization

  1. The asset allocations are highly sensitive to small changes in the inputs.
  2. Asset allocations tend to be highly concentrated.
  3. Investors are concerned with more than mean and variance of returns.
  4. The sources of risk may not be diversified.
  5. Disconnect between MVO and the influences on the value of the liability or consumption series it is intended to pay for.
  6. Single-period framework, no trading costs or taxes considered.

Mean-Variance Optimization formula

Um = E(Rm) – 0.005λσm^2

Um = the investor’s utility for asset mix (allocation) m

Rm = the return for asset mix m

λ = the investor’s risk aversion coefficient

σm^2 = the expected variance of return for asset mix m

The value of 0.005 assumes E(Rm) and σm are expressed as percentages rather than decimals.

Optional Allocation formula for a single risk-free and a single risky asset


λ = investor’s degree of risk aversion

μ = risky assets expected return

rf = risk-free rate of return

σ^2 = variance of return

The Fed model predicts that stocks are overvalued if…

…the forward earnings yield on the equity is less than the yield on Treasury bonds.

2 Reasons to use a bottom-up forecasting approach:

  • May provide the opportunity to identify attractively priced securities irrespective of the attractiveness of the sectors.
  • May be a better fit for the investors who focus on a market niche.

Bottom-up forecasts are often more ____ than top-down forecasts.