FINM 3008/6016 Portfolio Construction Tutorial #6

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FINM 3008/6016 Portfolio Construction

Tutorial #6 – Outline

Question 1: Evaluating a Value/Growth Equity Tilt

On the course Wattle site can be found the file “Tutorial #6 – Analysis File.xlsx”. The ‘Value-Growth Data’ worksheet contains month-end total return indices for value and growth ('style'), the overall Australian equity market, and an indicative total portfolio. The style indices are from MSCI, which are based on ranking stocks by P/NTA and P/BV respectively. Total portfolio returns are generated using similar weights to those used in earlier tutorials, but without any adjustment to mean returns (unnecessary under this exercise). We are going to use this data to investigate the impact on portfolio risk and return that a 10% value “tilt” would have had over the analysis period. A tilt refers to a position or bias in a portfolio towards some common factor, characteristic or other aspect. We are going to use this data to review the following:

A) Performance over specific holding periods – Once you have done the analysis, Panel A of the 'Value Tilt Summary' worksheet will collect data on the performance of value, growth, Australian equity market (AE Index) and the total portfolio over the analysis period. It also reports the impact of a 10% value tilt on performance at both the AE and total portfolio levels. Performance measures include average returns, standard deviation of returns, tracking error versus the benchmark portfolio without the value tilt, and an information ratio (IR = excess return / tracking error). We will be analysing three holding periods: monthly, 12-month rolling, and 36-month rolling.

B) Analysis of performance episodes –This involves cutting and dicing the data series into “episodes” where value outperformed growth, and vice versa. This analysis provides another perspective on a value/growth tilt, by focusing on the magnitude and length of the periods over which outperformance and underperformance accrues. The latter provides an alternative view of risk by measuring, when a value tilt underperforms, how large the pain was and how long it lasted. The analysis can be presented via both charts and summary statistics.

Part A: Analysis of Performance over Specific Holding Periods

Complete all time series of: (a) monthly tilted portfolio returns (columns R to U), (b) 12-month rolling returns (columns AD to AK), and (c) 36-month rolling returns (columns AM to AT), for the following:

· Value Index (already done for monthly returns – see column M)

· Growth Index (already done for monthly returns – see column N)

· Market Index (already done for monthly returns – see column O)

· Total Portfolio (already done for monthly returns – see column P)

· Australian equity (AE) portfolio with a 10% value tilt

· Total portfolio containing an AE portfolio with a 10% value tilt

· Tilted AE portfolio relative to market portfolio (Use: Relative Return = (1+TiltedAE)/(1+Market) -1)

· Tilted Total portfolio relative to benchmark portfolio (Use: Relative Return = (1+Tilted)/(1+Benchmark) -1)

Advice on Calculations:  

- You can think of an AE portfolio with 10% value tilt as comprising a 100% long position in the market, a 10% long position in the value index, which is funded by a 10% short position in the growth index. Thus: Tilted AE Portfolio Return = AE Index Return + 10% * Value Index Return – 10% * Growth Index Return.

- Do similar for the Total Portfolio, except you need to scale the tilt for the 30% AE weight to estimate the overall impact on the Total Portfolio, as follows: Tilted Total Portfolio Return = Total Portfolio Return  +  30% * 10% * Value Index Return – 30% * 10% * Growth Index Return.

- Columns W to AB headed ‘ln(1+R)’  contain continuously compounded returns, which you can use to construct 12-month and 36-month rolling returns by summing, and taking EXP()-1 . Alternatively, work directly from return indices (using index values 12- or 36-months apart). Do not annualize the return series themselves: annualization will be done when estimating the summary measures in rows 5 and 6.

Once the time series have been created, complete the calculation of the measures listed below assuming independent returns. The results are linked into Panel A in the ‘SUMMARY’ worksheet.

· Compound returns (pa) over the entire period (cells R5 to U5)

· Annualized standard deviation of returns (row 6)

· Annualized tracking error of both tilted portfolios (i.e. AE, Total) versus their benchmark (also row 6)

· Note: IR is estimated for you

Advice on Calculations:  

- In tutorial 2 you learnt the formula to calculate the difference between two geometric means. These can be used to calculate the difference between two compounded returns here (e.g. cell S5)

(Comment: Under the approach used here, we are focusing on the distribution of wealth at the end of 1-, 12- and 36-months, rather than the distribution of per annum returns over the holding period. As discussed in the text, these are NOT the same thing.)

Discussion points:

(i) What impact would a 10% value tilt have had on returns?

(ii) What impact would a 10% value tilt have had on portfolio ‘risk’? (Hint: Consider and contrast the various risk measures and holding periods - there is no single, unambiguous answer.)

(iii) Suppose that the outperformance by value is expected to continue over the long run. What type of investor might consider a value tilt to be a good idea

(iv) How might you decide how large a tilt is justified?

Part B: Analysis of Relative Performance Episodes

The previous analysis focused on risk over defined holding periods of 1-month, 12-months and 36-months. An investor might also be interested in how long and by how much a style tilt might lead to underperformance. One way of gauging this risk is to examine previous relative performance “episodes”. To do so, use the following procedure:

· Examine the relative return index chart (see ‘Value-Growth Chart' worksheet) - The chart provided is formed by taking the ratio of the value/growth indices. This chart can be used to visually identify the start and end points of outperformance phases by value versus growth, and vice versa. (You might ignore the shoulders of the data series, as these capture incomplete episodes.) How you define these periods is up to you: it will involve an element of judgment about what is significant to an investor. Hint: If you place the cursor over a point on the chart, you can get the x and y values to pop up on the screen.  

· Calculate the following summary statistics for each episode:

- length of episode in months and/or years

- cumulative relative performance over each episode

- annualized relative performance over each episode

· You can use columns H and I in the “Value-Growth Data” tab to help you calculate measures if you wish. Report the above measures by either: (a) including on the chart in the 'Value-Growth Chart’ sheet using a text box and arrows pointing to the episodes, or (b) placing data in the spaces provided in the ‘Value Tilt Summary’ worksheet (or both) - whatever you prefer.

· You might want to average these measures across the respective episodes of growth and value outperformance, to get a feel for the characteristics of an ‘average’ phase.

Discussion point: 

(v) How does the episode-based analysis influence your perception the risks of taking a value tilt? Does it make you more or less willing to adopt a style tilt?

Question 2: Emerging Markets

List the key ways in which emerging markets differ from developed equity markets.

· Worksheets ‘EM DATA’ and ‘Q2’ provide data and charts on both relative performance and current valuations (Price/Earnings and Price/Book Value). See tabs “Q2 – EM Relative Return Chart” and “Q2 – EM Relative value Chart”.