Performance Measurement

Distinguish performance measurement, attribution, and appraisal.

Performance measurement—what was the portfolio’s performance?

Performance attribution—how was the performance achieved?

Performance appraisal—was the performance achieved through manager

skill or luck?

Macro attribution vs micro attribution

Macro is evaluating the asset owner’s tactical asset allocation (how did a manager’s broad sector perform-sector allocation) and manager selection decisions (how did the manager’s own portfolio for that broad sector perform-selection + interaction). Micro is evaluating the impact of the portfolio manager’s decisions on the performance of the asset owner’s total fund (how did the manager allocate within the sub-sectors of his broad category-sector allocation)

Explain total-return based, holdings-based, and transaction-based attribution methods.

Total-return is most appropriate when holdings data is not readily available. Holdings-based uses holdings data per period, but results can be inaccurate if end of period prices differ significantly from actual transaction prices. Thus, holdings-based is more appropriate for passively-managed funds. Transaction-based is the most accurate and uses both holdings data and transaction data.

Effective attribution analysis must

reconcile to the total portfolio return or risk exposure.

Explain arithmetic vs geometric attributions

Arithmetic is just R-B, but it may not be accurate over multiple periods. Geometric uses (R-B)/1+B.

BHB model.

The asset allocation vs security selection breakdown is already covered in l2. BHB has another mathematically equivalent calculation. Instead of using w_p in security selection, use w_b. Then add a third component: the interaction effect. Ii = (wi − Wi)(Ri − Bi).

Differentiate BHB model with BF model.

Security selection is exactly the same. Sector allocation is now computed as sum (wi-Wi)(Bi-B), where B is benchmark portfolio return. Note that the math checks out exactly the same, but subtracting B gives further intuition. For instance, let’s say manager overweighted a -2% sector by 10% when overall market is 8.2%. He gets penalized 0.2% from overweighting a losing sector but also another 0.82% since that 10% is also an opportunity cost of not investing in the market.

Fixed income return attribution methods are

Exposure decomp: group by duration buckets, and compare their weights to benchmark.

Yield curve decomp - duration based: Decompose yield changes by level, slope, curvature, spread.

Yield curve decomp - full repricing: Decompose by spot rates.

Formulate curvature

Butterfly spread = 2*belly-long-short. A straight line has curvature 0. If spread is positive, the yield curve is concave, and a larger magnitude indicates more curvature. When spread is negative, the yield curve is convex.

How to select the appropriate risk attribution approach for bottom up, top-down, factor based methods using relative risk vs absolute risk.

Bottom up relative uses marginal contribution to tracking risk.

Bottom up absolute uses marginal contribution to total risk.

Top-down relative breaks down tracking risk to allocation/security selection decisions.

Factor-based relative uses factor’s marginal contribution to tracking risk.

Factor-based absolute uses factor’s marginal contribution to total risk.

what benchmarks do market neutral managers use?

Absolute return benchmarks. For instance, T-bill + a percentage is an absolute return benchmark.

Liability-based benchmarks

A recent innovation is LDI indexes, which are investible indexes designed specifically for portfolios intended to hedge pension liabilities. However, they may not describe a pension plan’s liability structure accurately.

Explain factor-model-based benchmarks, return-based benchmarks, manager peer group, and custom security-based benchmarks

Factor-model-based: Regress portfolio returns on chosen factors to get sensitivities, then predict expected return.

Returns-based: Same idea, but factors are style indexes and weights must be non-negative and sum to 1.

Peer-group: An issue with peer group that managers within the same category can still face vastly different constraints.

Custom Security-Based: After identifying the manager’s investment process, the benchmark is constructed by selecting securities and weightings consistent with that process and client restrictions.

Bailey and Tierney criteria for benchmark

Unambiguous, investable, measurable, appropriate, reflective of current investment opinions, Specified in advance (benchmark constructed prior to performance period), accountable (clients made aware of differences between portfolio and benchmark).

Derive and explain P = M + S + A

S=B-M, which is style return. A good benchmark should not show correlation between S and A. Define E=S+A. A good benchmark should show positive correlation between E and S.

Define normal benchmark.

The most appropriate benchmark for an investor’s investment process.

Issues that arise when benchmarking real estate include

Benchmarks include only a subset of the asset class.
Performance is self reported in peer group benchmarks
Appraisal indexes contains smoothing
Difference in leverage between benchmark and funds

Issues that arise when comparing returns of private equity managers include

Different methods of valuation, early loss/gain can significantly change IRR, companies in funds can be in diff stages of development.

Explain PME (public market equivalent)

It uses cash flow data to replicate the general partner’s capital calls and distributions, assuming these same cash flows were invested in the chosen equity index.

Difficulties in benchmarking commodities include

1: use of futures in indexes.
2: different degrees of leverage.
3: different weightings of commodities in indexes.

Formulate Sharpe and Treynor and their issues.

Sharpe is excess return over risk-free divided by portfolio volatility. It assumes indifference between upside and downside volatilities. Treynor divides by beta of portfolio and assumes a diversification.

Formulate appraisal ratio.

alpha divided by standard deviation of residuals. Both are derived from a factor regression.

Portfolio Y delivered an average annualized return of 9.0% over the past 60 months. The annualized standard deviation over this same time period was 20.0%. The market index returned 8.0% per year on average over the same time period, with an annualized standard deviation of 12.0%. Portfolio Y has an estimated beta of 1.40 versus the market index. Assuming the risk-free rate is 3.0% per year, the appraisal ratio is closest to

Solve for alpha using Jensen’s alpha first. 9-(3+1.4*(8-3))=-1. Then solve for residual std. 0.2²-1.4²*0.12² = 0.011776. -1/sqrt(0.011776)=-0.0922

Formulate Sortino ratio

Excess over minimum required return divided by downside semideviation.

Formulate capture ratio

Upside and downside captures are R(m,t)/R(B,t), where m is manager and B is benchmark. Then capture ratio is upside/downside. Geometric average is typically used for multiple data points.

Formulate cumulative drawdown and drawdown duration

Cumulative drawdown(m,t) = min([V(m,t) − V(m,t*)]/V(m,t*), 0). Drawdown duration is the time between start of drawdown and cumulative drawdown reaches 0.

Three components of manager selection process:

Universe (suitability, style, active vs passive), quantitative (Attribution/Appraisal, capture, drawdown), qualitative. Qualitative is further divided to investment due diligence (philosophy regarding inefficiency, process to exploit this inefficiency, people to implement the process, portfolio consistency) and operational (procedure

Why are decision makers more concerned with type i errors in manager selection?

Type i errors create explicit costs instead of opportunity costs in type ii.

Type i errors are easier to quantify.

Type i errors are more transparent to investors.

methods of style analysis and pros/cons

Return-based style analysis (RBSA) - same method as the return based benchmark discussed in a previous section. Simple to use, but portfolio sensitivities change over time, and loadings are average over regression period.

Holdings-based style analysis - Examine the styles of holdings. While more precise, it is only a snapshot and may not be appropriate for high turnover portfolios. It is also subject to window dressing.

Active share

½ ∑ | Strategy Weight_i − Benchmark Weight_i |

Explain capacity of inefficiencies when judging investment philosophy during the qualitative process.

Is the return sufficient and frequent enough to cover costs?
Is the return repeatable?

Is the return sustainable? At what asset level can the strategy no longer support?

What are the considerations when judging investment personnel?

Do they have enough expertise? Does the team have sufficient depth? Is there key person risk? What’s the incentive to maintain talent?

What are the biases in a group? What due diligence steps exist when judging investment personnel?

Groupthink, Authority Bias, Complexity Bias.

How large is the team?
How are decisions made?
What is the diversity?

Describe the four elements of investment process

Signal creation - Does the strategy rely on unique information? Does the strategy involve faster timing? Does the strategy involve superior interpretation of information?
Signal capture - What is the process to translate ideas to positions? What is it and is it repeatable?

Portfolio construction - This relates to risk management. How is portfolio allocation adjusted? Does the portfolio include stop losses? How are hedges implemented? Consider liquidity as well/;

What are the considerations when performing operational due diligence?

How does the firm protect against unauthorized trades? Do backup facilities exist? How does the firm protect again cyber attacks?

Regarding infrastructure, are third-party providers respected? Did the firm switch between providers frequently?

Regarding risk, does the firm have a risk officer? What is the procedure for breaches?

Regarding Firm, what is the ownership structure (independently owned has more autonomy but may lack financial support during crisis)? What is the breakeven AUM? Does the firm foster a culture of compliance? Has there been lawsuits involved?

What are the benefits of a SMA? What operational concerns exist?

Benefits include direct ownership of underlying securities, customization, tax advantages (unlike ETFs, SMAs can tax harvest on individual securities), transparency. Operational concerns include extra cost, tracking risk, investor behavior (micromanaging),

What is the operational due diligence when it comes to contract terms?

Liquidity and fees.

what are the issues with performance-based fees?

Upside is squashed, leaving a left-skew. A std measure understates volatility.
Firms on performance fees can struggle during underperformance, versus a standard fee structure.
Managers may be incentivized to take on extra risk.