FINM 3008/6016 Portfolio Construction Tutorial #4

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FINM 3008/6016 Portfolio Construction

Tutorial #4 – Outline

Question 1

On the course wattle site can be found the file “Tutorial #4 - Analysis File.xls”. You are to use this file to investigate the impact of the measurement interval and time period on the inputs to mean-variance analysis. We are also going to discuss some of the underlying fundamental drivers of the data, including market events and economic developments. The file contains various time series across a series of worksheets, from which you will be expected to generate certain measures and selected charts. As we will be examining returns spanning various time horizons, for this exercise we will perform the analysis on continuously compounded returns, i.e.     r_t = ln(P_t/P_t-1) = ln(1+R_t). This is the third learning-by-doing exercise that gives you exposure to spreadsheet-based analysis of real data, including creation of charts, and will help prepare you for the assignment.

Part A: Impact of Measurement Interval

Commence by completing the estimate for the measures listed below. The estimates should be placed in the shaded cells appearing in the various worksheets, which are in turn linked to the “SUMMARY” worksheet.  

(i) Annualized standard deviation for all 9 asset classes on returns over the following measurement intervals:

· Monthly

· Quarterly (i.e. 3 months)

· Yearly (i.e. 12 months)

· 3-year (i.e. 36 months)

· 5-year (i.e. 60 months)

(ii) Serial correlation on monthly, quarterly and yearly returns, for all 9 asset classes.

(iii) Correlations between: Australian Equities and Listed Property (AE vs LP), Australian Equities and Direct Property (AE vs DP), and Listed Property and Direct Property (LP vs DP); all over the same 5 different measurement intervals listed under part (a).

Notes:

- To estimate an annualized standard deviation, calculate variance, scale by time to annualize (e.g. multiply monthly variance by 12; divide 3-yearly variance by 3, etc), and take the square root. An example for AE appears in cell M5 of the “Monthly Returns” worksheet. (Comment: Monthly and quarterly standard deviations are being annualized under the assumption of independent returns.)

- Formulas can be copied both within and across worksheets. (Copying across worksheets works if they are set up exactly the same. Adjustments need to be made to the annualization factor for part (a).)  

- Please have a look at the formulas and try to understand them (rather than just copying them blindly). An important part of the learning process is coming to grips with what is going on.

- The data provided is based on ‘rolling windows’. These series reveal the distribution of estimates across various holding periods that have occurred during the sample period. Rolling estimates are acceptable for the task at hand. However, use of overlapping observations means that the estimates themselves will be serially correlated, which would have implications if the main focus was statistical significance of these estimates.

Discussion points:

(a) The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?  

(b) What considerations might you take into account in deciding the appropriate measurement interval?

Part B: Measurement Time Period

The ’10-year rolling stats’ worksheet contains time series of 10-year (i.e. 120-month) rolling estimates for.   

· Standard deviation (annualized) of all 9 asset classes

· Correlations

- Australian equities versus all other 8 asset classes

- World equities (hedged) versus world fixed income (which is also hedged)

- World equities (unhedged) versus commodities (which is also unhedged)

The mean, standard deviation, maximum and minimum for the various time series appear at the top. Examine these to get a sense for distribution of the series, i.e. how variable they can be across 10-year windows.

Generate five charts containing the series listed below:

· 10-year rolling standard deviation:

- Australian equities

- World equities, unhedged and hedged on same chart (Note: This chart is provided as a template. You can copy it, and change references, headings, etc to create other charts.)

- Listed property and world fixed income on same chart

· 10-year rolling correlation:

- Australian equities vs Australian fixed income; world equities (hedged) vs world fixed income (both series on one chart)

- World equities (unhedged) vs commodities

- Australian equities vs World Equities (unhedged); Australian equities vs World Equities (hedged) (both series on one chart)

Note: A chart of the 10-year rolling correlation of AE with WFI appears in the file, as well as an additional worksheet. These are to highlight the impact that one outlier can have on the measurement, specifically related to the equity market crash of October 1987, and may be discussed in class if time permits.

Discussion points:

(c) What might be causing the instability in estimates observed in the series you have plotted? In particular, think about what ‘real’ forces might be operating, and how they may be reflected in the statistics through time.

(d) What considerations might you take into account in deciding the appropriate measurement period?