BFF2701 Chap.7 Portfolio and Execution Performance
Portfolio and Execution Performance
Performance evaluation begins by matching the measure to the risk and decision being assessed. The Sharpe ratio uses excess return per unit of total volatility, so it suits an entire portfolio where total risk matters. The Treynor ratio uses excess return per unit of beta, so it focuses on systematic risk and is more meaningful for a well-diversified portfolio.
Jensen alpha compares realised return with the return implied by systematic exposure under the selected model. None of these measures is a complete verdict: benchmark period, risk-free rate, estimation window and leverage can change the ranking. Execution measures ask a different question.
VWAP compares a fill with the market's volume-weighted average price, while implementation shortfall compares the realised portfolio outcome with the price when the investment decision was made. Implementation shortfall can include explicit costs, delay, market impact and the opportunity cost of unexecuted shares. A favourable VWAP result can coexist with poor implementation shortfall if the market moved before execution.
State the perspective, sign convention and benchmark before computing.
What this chapter covers
- 01
Sharpe ratio and total risk
- 02
Treynor ratio and systematic risk
- 03
Jensen alpha
- 04
Benchmark selection
- 05
VWAP execution comparison
- 06
Implementation shortfall
- 07
Delay, impact and opportunity cost
Worked example · free
Compare Sharpe and Treynor rankings
- +2Portfolio A excess return = 11% minus 3% = 8%. Its Sharpe ratio = 8% divided by 10% = 0.80.
- +2Portfolio B excess return = 13% minus 3% = 10%. Its Sharpe ratio = 10% divided by 16% = 0.625.
- +1Portfolio A Treynor ratio = 8% divided by 0.8 = 10% excess return per beta unit.
- +1Portfolio B Treynor ratio = 10% divided by 1.0 = 10% excess return per beta unit.
- +2Sharpe ranks A above B because A delivers more excess return per unit of total volatility. Treynor ties them because their excess returns scale equally with beta.
- +1Use Sharpe when total portfolio risk matters; use Treynor only when systematic risk is the appropriate denominator, typically for diversified portfolios.
Key terms
- Sharpe ratio
- Excess return per unit of total return volatility.
- Treynor ratio
- Excess return per unit of systematic risk.
- Jensen alpha
- Return above or below that implied by a systematic-risk model.
- VWAP
- The volume-weighted average transaction price over a specified interval.
- Decision price
- The market price when the investment decision is made.
- Implementation shortfall
- The performance gap between a paper portfolio at the decision price and the realised outcome.
Portfolio and Execution Performance FAQ
When should I use Sharpe rather than Treynor?
Use Sharpe when total risk is relevant, especially for a stand-alone portfolio. Treynor is better suited to systematic-risk comparison among well-diversified portfolios where idiosyncratic risk is already controlled.
Can positive alpha prove manager skill?
No. Alpha depends on the selected model, data period and estimation quality. Costs and statistical uncertainty also matter, so a positive estimate is evidence to examine rather than proof of skill.
Why can VWAP and implementation shortfall disagree?
VWAP benchmarks against trading during the execution window. Implementation shortfall begins at the earlier decision price and can capture delay and missed trades that the selected VWAP interval excludes.
How should a buyer report execution cost?
Declare the sign convention, then report worse-than-benchmark prices as positive costs or negative performance consistently. Do not switch conventions mid-answer, and reconcile every component to the reported total.
Which benchmark holds an execution desk accountable?
The answer depends on the decision the desk controls. VWAP evaluates fills against market trading during a stated interval, while implementation shortfall can include movement from the earlier decision price, delay and missed quantity. Name the responsibility and time origin before choosing the benchmark, then explain what the alternative would omit.
Exam move
Build a decision tree for denominator choice: total volatility leads to Sharpe, beta leads to Treynor, and expected return conditional on beta leads to Jensen alpha. Keep portfolio performance separate from execution quality. For VWAP or shortfall, write the benchmark time, trade direction and sign convention first.
End each calculation with a ranking and a limitation, because the same strategy can look different under another benchmark. Prepare one portfolio table containing return, risk-free rate, volatility and beta. Compute Sharpe and Treynor from the same data, then explain any ranking disagreement through the denominator rather than choosing the more flattering result.
Add Jensen alpha only after writing the expected-return model and verifying that returns and rates use the same period. For execution, make a separate timeline from decision to order release, fills and close. VWAP weights market prices by market volume within the chosen interval; implementation shortfall starts from the decision benchmark and can include delay, impact, fees and missed quantity.
Reconcile every component to the total under one sign convention. Test benchmark sensitivity by moving the VWAP interval or decision time and explaining what information the new comparison excludes. This exposes why a buyer can beat VWAP yet still suffer positive implementation shortfall after a pre-trade price rise. A final recommendation should say which benchmark aligns with the manager's responsibility.
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