CFA Level III · Level III Core

Asset Allocation to Alternative Investments: formula sheet

Full chapter guide

Key formulas

Unsmoothing appraisal returns (first-order): r(true, t) = [r(obs, t) − φ × r(obs, t−1)] ÷ (1 − φ); φ is the smoothing parameter (0 ≤ φ < 1). Unsmoothed volatility is higher than observed volatility. Use only when the question gives φ.
Portfolio variance, two assets: σp² = w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2; Lower correlation ρ means more diversification. Understated σ or ρ for alternatives overstates the benefit.
Net return after fees: Net return = Gross return − management fee − performance fee; Performance fee = incentive rate × profit above any hurdle. Always compare alternatives on a net-of-fee basis.
Leveraged return: R(levered) = R(asset) + (D ÷ E) × [R(asset) − cost of debt]; D ÷ E is debt to equity. Leverage magnifies losses as well as gains.
Desmoothing (Geltner) of appraisal returns: R*(t) = [R(t) − φ × R(t−1)] ÷ (1 − φ); R(t) is the observed smoothed return, φ is the smoothing parameter (the weight on the prior value), and R*(t) is the estimated true return. φ is often estimated from the first-order autocorrelation of the observed returns. Valid for 0 ≤ φ < 1.
Effect of desmoothing on volatility: Compute σ(true) as the standard deviation of the desmoothed series R*(t); Do not scale observed volatility with a shortcut factor. Desmoothing raises measured volatility when φ > 0, so check that the standard deviation of R* is higher than that of the observed returns.
Portfolio variance (two assets): σp² = w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2; Understated σ and ρ from smoothing reduce σp² and bias MVO toward alternatives.
Net return after fees: Net return = Gross return − management fee − incentive fee; Compute the incentive fee on the base the contract states, such as profit above a hurdle. Use the stated order of fees.
Unsmoothing appraisal returns: r(true,t) = [r(obs,t) − (1 − λ) × r(obs,t−1)] ÷ λ; This inverts a first-order smoothing model: r(obs,t) = λ × r(true,t) + (1 − λ) × r(obs,t−1). Here λ is between 0 and 1 and is the weight on the current period's true return. The rest of the observed return is carried over from the previous observed return. One unsmoothed observation does not prove that volatility is higher. Volatility is higher when you unsmooth the whole series, because smoothing damps the swings.
Smoothed volatility understatement: σ(true) > σ(reported) when returns are smoothed; Higher true volatility and higher true correlation with equities reduce the apparent diversification benefit and the apparent Sharpe ratio.
Commodity futures return: Total return ≈ spot return + roll yield + collateral return; Roll yield is positive in backwardation and negative in contango, other things equal.
Unfunded commitment exposure: Illiquid exposure if all commitments are called = NAV invested + unfunded commitment; Unfunded commitments are not extra assets today. They are claims on liquid assets that are still held. This sum is the economic exposure, and it equals the illiquid share of total assets once all commitments are called (ignoring distributions and growth). Use it to judge the true size of the private allocation and its liquidity demand.
Unfunded commitment: Unfunded commitment = Total commitment − Paid-in capital (capital called to date); Capital returned as distributions does not reduce the unfunded amount unless the fund agreement allows it to be recalled.
Net asset value (NAV) of an investor's fund stake, simplified: Ending NAV = Beginning NAV + Capital calls + Investment gains − Distributions − Fees and expenses; Use this to project exposure each year in a pacing question.
Overcommitment ratio (illustrative measure): Overcommitment ratio = Total commitments ÷ Target invested amount; A value above 1 means overcommitment. It increases funding risk. This is an illustrative measure, not a standard CFA Institute formula.
Fund-level return after leverage: Levered return = Asset return + (D ÷ E) × (Asset return − Cost of debt); D ÷ E is debt to equity. Leverage magnifies both gains and losses. For positive leverage (D/E > 0), the levered return falls below the asset return whenever the asset return is lower than the cost of debt.
Incentive fee with hurdle and catch-up (idea): Carry = Carry % × Profits above hurdle, or Carry % × Total profits once the full catch-up is reached; Read the question for whether there is a catch-up, and whether it is full or partial. Compute only what the stated terms say.
Net return to investor: Net return = Gross return − Management fee − Incentive fee − Other expenses; Compare managers on net returns, not gross.

Quick revision

Alternatives are used for diversification, return enhancement, inflation protection and access to other risk premiums.
Smoothed returns understate volatility and correlation with other assets.
Unadjusted optimization on smoothed data tends to overallocate to illiquid assets.
Unsmoothing returns raises estimated volatility and usually raises correlations.
Illiquid holdings must fit the client's liquidity needs, time horizon and governance capacity.
Unfunded commitments to private funds create future cash calls that must be planned for.
Risk budgeting allocates by contribution to risk rather than by capital alone.
Hedge fund categories differ widely in risk, so do not treat them as one asset class.
Fees, including management and performance fees, reduce net returns and must be judged on a net basis.
Due diligence covers the manager, strategy, operations, risk, terms and alignment of interests.
Always link the recommendation to a stated objective or constraint.
In essays, answer the command word and give only the number of responses requested.

Common mistakes

Treating observed alternative volatility and correlation as true risk. Fix: Say that smoothing understates risk and overstates diversification. Unsmooth the returns if a parameter is given.
Recommending alternatives only because they raise expected return. Fix: Always test liquidity, horizon, governance and risk tolerance before recommending, and explain the match.
Saying smoothing raises measured volatility. Fix: Remember that smoothing hides moves, so measured volatility and correlation are too low and the Sharpe ratio is too high.
Applying the desmoothing formula with the wrong sign or forgetting to divide by (1 − φ). Fix: Write R* = (R − φ × prior R) ÷ (1 − φ) and check that the result is more volatile than the input.
Treating hedge funds as one asset class with one risk and return profile. Fix: Name the strategy and its main risk exposure, such as equity beta, credit or liquidity risk, before judging fit.
Accepting low reported volatility and correlation for private assets as true diversification. Fix: Say the data are smoothed, that true risk and correlation are higher, and adjust or flag it before sizing the allocation.
Treating the liquidity budget and liquidity risk as the same thing. Fix: Remember: the budget is the plan of cash sources and uses. Liquidity risk is the risk that the plan fails. Say which one you mean.
Ignoring unfunded commitments when judging how much liquid cash a client needs. Fix: Add the unfunded amount to the exposure and treat it as a future cash call that the client has legally agreed to fund.

Exam tips

In constructed response, tie every reason to the client. A generic list of alternative traits earns few points.
Match the command word: 'justify' needs a reason, 'calculate' needs the number shown, 'discuss' needs two or more linked points.
When a question gives low volatility or low correlation for private assets, check for smoothing before accepting the diversification claim.
Always mention liquidity and time horizon when sizing illiquid allocations.
For item sets, eliminate options that ignore the binding constraint.
Link every weakness to its effect on inputs: lower volatility, lower correlation, higher Sharpe ratio, overweighting.
Show the desmoothing formula and the numbers; a correct number alone earns credit, but working protects you from slips.
When asked to justify a method, name the client's constraint it addresses, such as liquidity needs or horizon.