FINM 3008/6016 Portfolio Construction Tutorial #5

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FINM 3008/6016 Portfolio Construction

Tutorial #5 – Outline

Question 1: Analysis of Portfolio Adjustments

On the course Wattle site can be found the file “Tutorial #5 - Analysis File.xlsx”. This file contains quarter-end total return indices in A$ for eleven asset classes, and some benchmark portfolio weightings. A linked ‘SUMMARY’ worksheet and plus other partially completed worksheets are included. (The cells you need to complete are shaded.) You are to use this file to investigate the impact under mean-variance analysis of making adjustments to an existing portfolio. This is the final in the series of learn-by-doing exercises aimed at building skills needed for the Assignment. In particular, this tutorial question shows you how to conduct an analysis to demonstrate how any recommended changes can improve expected portfolio outcomes. While the analysis here focuses on mean-variance outputs and quarterly return data, the general approach can be readily extended to incorporate other portfolio objectives and differing data.

Part (A): Establishing the baseline for analysis

The first task is to establish the baseline portfolio for analysis, which will comprise a ‘benchmark’ portfolio (perhaps the investor’s current portfolio, or the peer group portfolio), plus a set of assumptions about asset risk and return. The starting point for these assumptions is the condition that each asset offers an expected return that is consistent with the risk that it contributes to the benchmark portfolio, where risk is measured from the historical data series provided. The contribution to risk will be measured by the beta versus the benchmark portfolio. This is the ‘implied views’ method discussed in Lecture 4. The suggested approach to adjusting the mean returns and generating the baseline portfolio is as follows:

· In the worksheet ‘Benchmark, Betas, Returns’ is found the series of quarterly asset returns, estimated via linking to the ‘Total Return Index QTR’ worksheet. The SUMPRODUCT function is used to combine asset returns with the weightings provided (appearing in row 3) to derive historical quarterly returns on the benchmark portfolio (appearing in column M).

· Within this worksheet, you need to estimate the beta of each asset class versus the benchmark portfolio. This can be done using the SLOPE function. Beta estimates are to appear in cells B4 through L4. These betas provide a measure of the risk of each asset in the context of the benchmark portfolio.

· You now need to estimate E[R] for each asset as a function of beta. We are going to assume R_f = 0.838% per quarter (broadly in line with current Australian short-term rates - see comment in cell N9), and a (portfolio/‘market’) risk premium of 1.5% per quarter (see comment in cell O9). Together, these imply an expected return on the benchmark portfolio (E[R_BP]) of 2.34% per quarter, or around 9.35% per annum. Use the CAPM equation to estimate ‘target’ expected returns for each asset, as if the benchmark portfolio is the “market portfolio”. These estimates are to appear in cells B6 through L6. When this is done, the required adjustment to the mean will appear in row 11.

· The worksheet ‘Adjusted Returns’ should now contain mean-adjusted quarterly asset and portfolio returns. It also calculates the following summary statistics for the benchmark portfolio over the period

- Mean returns: quarterly and quarterly * 4  (latter is a very rough method of annualizing; a guide only)

- Standard deviation: quarterly and annualized (latter assumes independence, hence approximate)

- Sharpe ratio: based on quarterly mean and standard deviation.

Comments:

- For this exercise, we are analyzing portfolio outcomes over quarterly holding periods. Hence we adjust the arithmetic mean of quarterly holding period returns. In earlier tutorials, we adjusted the geometric mean towards a particular target. In these cases, the focus was compound returns over multiple periods, often with differing investment horizons. The best method depends on the objective and circumstances.

- The benchmark portfolio should be M-V optimal at these returns for this particular set of assets. That means if you estimate the optimal (i.e. maximum Sharpe ratio) portfolio using these inputs, you should get back the same portfolio weightings you started with. If you are interested in establishing this for yourself, refer to the ‘Portfolio Check’ worksheet.

Discussion points for part (A):

a) Do the implied expected returns, as estimated by reference to beta, make economic sense?

b) In instances where the expected returns do not seem reasonable, how might you respond in order to establish a more reasonable basis for analysis?

Part (B): Data-based (non-parametric) analysis of adjustments to the baseline portfolio

Analysis – The worksheet ‘Analysis - Data Based’ has been set up to analyze the impact on portfolio risk and return from making changes to the asset allocation. Have a look through this worksheet to understand the structure. It contains quarterly asset and benchmark portfolio returns, plus an adjusted portfolio return series (column N) that arises when a vector of adjusted portfolio weightings (cells B5 to L5) are applied over the analysis period. Input cells B4 to L4 facilitate +/- adjustments to the benchmark portfolio weightings, which should sum up to zero (cell R21 tells you if they don’t). Summary statistics are calculated for both portfolios. Output appears in cells Q19 to AH19 that can be copied into the shaded cells below, which in turn are linked to the ‘SUMMARY’ worksheet. Use the worksheet to analyze the impact of the following asset weighting changes:

· Switch -10% from AE into WE (+6% unhedged, +4% hedged).

- Initially do the switch at the existing return assumptions.

- Repeat the switch after adding +0.50% per quarter (about 2% pa) to returns for both WE series. This might be taken as a examining the view that WE looks more attractive than suggested by ‘implied views’. Do the adjustment by adding +0.5% to cells C7 and D7 in the “  - Adjustment” row appearing in line 7 within the ‘Benchmark, Betas, Returns’ worksheet, then reverse it afterwards. (After the analysis is complete, also reverse the switch from AE into WE so weights are back to the baseline). Note: here we are combining implied views with our own beliefs about asset returns (that WE will outperform the implied views estimate by 2% p.a.). This is an example of the mixed-estimation techniques outlined in Lecture 4.

· Introduce a 10% weighting to commodities into the portfolio, after adjusting upwards their E[R]

- Adjust commodity return upwards by 0.33% per quarter. Do the adjustment by adding +0.33% to cell H7 in the “  - Adjustment” row 7 in the ‘Benchmark, Betas, Returns’ worksheet. (Note: After the analysis is complete, reverse the adjustment). This amounts to imposing the assumption that COMM can generate a return of 2.17% pa higher than Cash

- First, fund the commodity investment from all assets (reduce other assets by -0.10 * benchmark weight)

- Then, fund from equities as follows: -5% AE, -3% WE, unh, -2% WE, h

- Finally, fund from fixed income as follows: -5% AFI, -5% WFI

Discussion points:

c) Do the two switches improve the portfolio outcomes?

d) Comment on the usefulness and reliability of this type of (data-based) analysis.

Part (C): Parametric analysis of adjustments to the baseline portfolio, and general discussion

Analysis – You are now going to use the ‘Analysis - Parametric’ worksheet to conduct a similar analysis based on directly estimating the summary statistics from an expected return vector and a covariance matrix. The parametric approach permits evaluation of assets for which a full data history does not exist, providing you can form estimates for expected returns and covariance. (Comment: In practice, the covariance matrix is often derived from estimates of standard deviations and correlations.) 

The worksheet has been completed for you. It is highly recommended that you look at how it is constructed as a learning exercise. (As part of the tutorial material, the methods are examinable!) Points to note:

· Cells O9 to Y9 calculate the asset E[R]’s from the adjusted returns, while cell Z9 estimates portfolio E[R]. (Note that these equal the E[R]’s initially calculated using implied views in Part A, which they should by design. When you experiment with this at home, if this is not the case it may be because you still have adjustments in line 7 within the ‘Benchmark, Betas, Returns’ worksheet)

· In estimating the portfolio standard deviation, a weighted covariance matrix for N assets is formed as follows:

- Cells O13 to Y23 contain an N*N matrix of squared weightings with respect to each cell of the covariance matrix, i.e. _wi x _wj. Have a look at how this is done, keeping in mind the formula for portfolio variance.  

- Cells O27 through Y37 contain an N*N covariance matrix, estimated from the adjusted asset return data using the COVAR function. Again, have a look at how this is done, keeping in mind the formula for portfolio variance.  

- The variance of the portfolio appears in cell Z27, by taking the SUMPRODUCT of the above matrices.

The worksheet is set up in a similar fashion to the ‘Analysis - Data Based’ worksheet. It allows you to adjust the asset weightings (cells O5 to Y5), which generates new estimates appearing in cells AD7 to AH7, which can then be pasted and stored into the shaded cells below which are again linked to the ‘SUMMARY’ worksheet. Use this worksheet to estimate the impact of the following changes in asset weightings:

· Introduce a 10% weighting to emerging markets (EM). Fund the investment from all equities as follows:          -5% AE, -3% WE, unh, -2% WE, h. (After the analysis is complete, reverse the switch so weights are back to the baseline).

· Introduce a 10% weighting to index-linked bonds (ILB). Fund the investment from fixed interest as follows:      -5% AFI, -5% WFI.

Discussion points:

e) What benefits arise from adding these two new assets to the portfolio?

f) Is there any relative advantage to either the non-parametric or parametric approach?

g) How might you deal with new assets where there is no available history whatsoever?

Question 2: Alpha or Beta?

To what extent might the following investments deliver ‘alpha’ versus ‘beta’, or something else? (Base your answers around the ‘industry definition’ of beta and alpha.)

a) Enhanced passive equity fund, that is based around replicating a market index (e.g. S&P 500, S&P/ASX 300), but deviates occasionally from index weight when there is profit to be made. For instance, they may try to exploit temporary mispricing due to pressures stemming from large orders by other players (kind of a market-making or liquidity provision role); arbitrage between different classes of securities in the same company; or take advantage of IPOs (initial public offerings).  

b) Long-short hedge fund where each $1 of capital is invested in cash, but is used to support up to +$5 in long and -$5 in short equity positions.  

c) Macro hedge fund that takes market-timing positions based on macroeconomic views.

d) Opportunistic direct property fund that engages in property acquisition and development.