Thursday 31 August 2006

Quo Vadis?

If you're aything like me, incorporating the level of risk that you believe you're comfortable with into your asset allocation could still result in unpleasant surprises in the long run.

I've often read that for the long-term investor, time heals all wounds - that is, while equity investments may have large year-on-year variation in performance (a.k.a. "risk"), over long periods of time this variability "evens out" and the long-term performance will display less variation. That is, "risk" decreases over time.

However, I'd recently read a contrary view (unfortunately I can't recall the reference) which stated that time won't decrease the amount of variation (in dollar terms) in your final outcome. This seems to be at odds with the generally accepted view, but in fact it is just a different way of looking at the expected results - concentrating on the variability in the final dollar value of your portfolio rather than in the percentage average return overall.

While it is true that over time the average return will tend closer to the expected long-run value over time, this does NOT mean that in the long run your portfolio will end up with a final value close to what you thought you could reasonably expect. Due to the effect of compounding, over longer time horizons even small variations in average return have a big result.

Even though I was aware of this fact (and have an understanding of the "magic of compounding") it really didn't hit home for me until I ran some simulations of my portfolio (using my current investment mix and projected returns and std deviations loosely based on data from Portfolio Solutions)

It turns out that while the most likely outcome is as I'd expected (around $3 million AUD by the time I retire around 2027), there are several "outlier" scenarios where the end value of my portfolio would be less than $1 million - which is pretty depressing compared to my current net worth and what I could achieve by just investing the entire portfolio in "safe", fixed interest assets! Of course, with my current portfolio mix there is a similar probability that I could end up with over $5 million.

Before we look at the results of my modelling (done in excel) I should point out that it was a bit rough and ready. I had to use guestimates as to reasonable return and std deviation values to use for my "alternate" investments (gold, agribusiness trusts, coins) and "hedge" funds (OMIP series and Macquarie Equinox Select Opportunities). For the other asset types I adapted the values listed by Portfolio Solutions. Because I didn't have any information on covariance between by investments I've lumped all assets of the same class together (ie. All Australian share holdings are lumped together as one total amount, combining my superannuation funds, direct share holdings and geared share fund investments in my model). Hopefully any covariance errors should largely cancel each other out - lumping the like investments together assumes a covariance of "1", whereas they would really have a value slightly less than "1". And the model also generates each years return for each different asset type independantly, based on the asset types return and std deviation values and the amount invested at the start of the year (see this site for an excel formula that can be used for modelling normally distributed returns using mean and std deviation values). This means that the different asset classes have an implied covariance of "0", when in fact some would have a covariance value in the range 0-1 (eg. Australian and International shares), and some of the others would have negative covariance values. According to MPT by having a mix of assets my total portfolio should have significantly less risk than shown in the model. But this is still good as a "worst case" scenario. If I get in the mood I may attempt to calculate return and risk values to use for my Hedge and Alternate investment classes using the monthly unit price data I have for OMIP funds etc.

I think the main take-home lesson from this exercise is to remember that ANY one of the projected scenarios is equally likely to happen, but that you'll only get one bit at the cherry. So you could end up with one of the less likely outcomes - either very good or very bad. While looking at average results and the most likely outcome is useful for planning purposes, if you are taking on increased risk in order to achieve higher returns, you have to have a hard look at what the end result could actually be, and be comfortable with whatever happens. Que Sera, Sera!

Table 1: My current Portfolio Asset Mix

ASSET Gearing Annual Expected Performance
Type PV % Mix (Loan) Addition LVR Return Risk (std dev)
Au Shrs $595,596.00 34.5% $262,719.20 $ 8,299.35 44.1% 8.00% 17.00%
Int Shrs $232,864.00 13.5% $ 92,572.80 $ 6,453.95 39.8% 8.00% 15.00%
Au Prop $761,770.00 44.1% $350,554.00 $13,559.70 46.0% 7.50% 14.00%
Hedge $ 88,100.00 5.1% $ 57,620.00 $ 0.00 65.4% 11.00% 20.00%
Fixed Int $ 2,770.00 0.2% $ 554.00 $ 0.00 20.0% 5.00% 3.00%
Alternate $ 44,500.00 2.6% $ 0.00 $ 0.00 0.0% 3.00% 3.00%

Excel Formula for calculating a random return from an assets expected return and standard deviation:
Rn = SQRT(-2*LN(RAND()))*COS(2*PI()*RAND())

Figure 1: A plot of two runs of the model showing the degree of variability over time.

Figure 2: A plot of the first 32 out of 200 simulations.

Figure 3: A histogram of the end value of my Portfolio in 200 simulations.

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