Showing posts with label Investment Theory. Show all posts
Showing posts with label Investment Theory. Show all posts

Sunday, March 10, 2024

The Baseline Matters When Computing Long-run Investment Performance

I am expecting my rate of return over the last 20 years to look bad this year because 2004 was such a good year. In 2004 I gained 42.4% compared to a 13.7% gain for the MSCI World Index (in AUD terms). It was my best year ever in terms of investment performance. The ASX 200 gained 30.3%. You can already see this in this chart:

In 2023 my performance over the last 20 years almost matched the MSCI World Index's performance over the previous 20 years. But this year I am lagging a lot. Why did I do so well in 2004? It was mainly due to leveraging Australian shares. This table shows the AUD gains in 2004 for each investment:


The CFS Geared Share Fund is a levered Australian share fund. It provided the majority of gains. Nowadays I feel that I can't handle that much volatility. The fund is still available. Of these investments I am currently, 20 years later, invested in CFS Developing Companies, Platinum Capital, CREF Social Choice, and TIAA Real Estate.

I started 2004 with a net worth of AUD 170k and ended with AUD 298k.


Tuesday, February 20, 2024

When Does Our Investment Strategy Add Value?

EnoughWealth wonders if our investment strategy only adds value under certain market conditions. As a first step let's look at when the out-performance relative to the 60/40 portfolio happened:


The graph simply takes away the monthly return on the Vanguard 60/40 portfolio from Moom's actual results. We see there are periods of out- and under-performance throughout the period. Not surprisingly, it was weaker in 2023 in particular. I didn't do well in implementing the target portfolio strategy last year. Here is a graph comparing the performance of this theoretical portfolio and the Vanguard portfolio:


This looks more consistent. This portfolio is theoretical because it consists of a mix of actual investible funds and non-investible indices.

Bottom line, is I think it is a good idea to add things like managed futures, gold, real estate etc to your portfolio. It makes a real difference.

Sunday, February 18, 2024

A 60/40 Australia-Oriented Passive Benchmark

If we create a portfolio invested 50% in VDBA and 50% in VDGR we can simulate a 60/40 passive benchmark:

This requires monthly rebalancing of the portfolio. We ignore the costs of this rebalancing. Over this period, the benchmark portfolio had a compound annual return of 5.60% with a monthly standard deviation of 2.55% compared to Moom's compound return of 7.77% with a monthly standard deviation of 2.32%. Moom's beta to this portfolio was 0.8 with an annual alpha of 2.9%.

Note that our portfolio goes through three different "regimes" during this period. Up to October 2018 we had a portfolio that was about 60% long public equity. Then we received a large amount of cash, which we converted to bonds and then gradually invested in other assets. This phase lasted up to the end of 2020. Since then we have been close to the target portfolio.




VDGR

Following up on my comparison of our portfolio to VDBA, here is a comparison to VDGR. VDGR is a 70/30 mix, while VDBA is 50/50 and our portfolio is 60/40.

First, here is how $1000 would have evolved if invested either with me or in VDGR since the end of November 2017:

Put another way, the average annual return over this period was 6.97% for VDGR and 8.65% for Moom. 

VDGR is less conservative, but still underperformed. The monthly standard deviation of returns for VDGR is 2.84%, while it is 2.28% for Moom. So, we had higher returns with lower risk.

I again did a CAPM style analysis using the RBA cash rate as the risk free rate and treating VDGR as the index. Moom has a 0.72 beta to VDGR and an annual alpha of 2.58%.

Again, I conclude that the additional diversification in our portfolio really does add value.
 


Does My Investment Strategy Add Value?

EnoughWealth commented on my recent post on our target allocation:

"Have you tried benchmarking your actual and target asset allocation performance against something a lot simpler - like a basic Bond:Shares allocation with similar risk level, with appropriate split of AU vs Global within each and a basic index fund proxy for each? I just suspect you may not be adding a lot of performance by the degree of complexity and number of individual holdings. I did a quick comparison of your NW monthly figures to mine (after converting my figures using the relevant monthly avg AUD:USD exchange rate), and aside from the jump in my nW in Feb '23 when I updated my estimated valuations for non-home real estate values, the monthly and three year trend is visually almost identical -- if anything yours seem to have more volatility than mine. Since most of the individual investments in your portfolio have internal diversification, I'm not sure your role as an active fund manager of your own investment portfolio is actually adding much 'alpha' ;) Then again, your spare time is 'free' so at least you aren't charging yourself a fee as fund manager (on top of whatever fees are embedded in some of those funds you've chosen)."

My response was that I had a beta of less than one to the ASX 200 and had positive alpha... But I have now done an analysis that I think is close to what EnoughWealth is suggesting here. I picked the Vanguard managed ETF VDBA.AX, which is diversified across Australian and global stocks and bonds. So, this is a potential alternative to our current investments. It is 50/50 stocks and bonds, whereas I am targeting 60% equities. But we could lever it up a little bit if we wanted.

Vanguard nicely provide all the data needed. Most of the work is in calculating dividend reinvestment. I assumed dividends were reinvested on the ex-date increasing the number of shares. Then I multiplied the daily price by number of shares to get the total value. I carried out my analysis using month end values since inception of VDBA.

The results might surprise Bogleheads :)

First, here is how $1000 would have evolved if invested either with me or in VDBA since the end of November 2017:

Put another way, the average annual return over this period was 5.06% for VDBA and 8.65% for Moom. 

Is this because VDBA is a bit more conservative? As you can see from the graph, volatility is about the same for the two investments. Formally, the monthly standard deviation of returns for VDBA is 2.32%, while it is 2.28% for Moom. So, it's not because of that.

So, I also did a CAPM style analysis using the RBA cash rate as the risk free rate and treating VDBA as the index. Moom has a 0.88 beta to VDBA and an annual alpha of 3.33%. 1% of extra return on a $5 million portfolio is $50,000...

In conclusion, the additional diversification in our portfolio really does add value.
 


Sunday, January 21, 2024

How Much Investment Income Do We Need to Compensate for Inflation?

 


This chart compares the fitted investment income curve from my previous post about the "boiling point" with the monthly loss of value of our portfolio (including our house) due to inflation. I just took the monthly percentage change in Australia's consumer price index and multiplied by the value of our portfolio that month. The gap between the blue and orange curves is a naive estimate of how much can be spent each month in retirement mode.

Currently, projected investment income is only just enough to cover the loss from inflation. Smoothing inflation over twelve months tells a similar story:

Here I divide the CPI by its value twelve months earlier, take the twelfth root and subtract one before multiplying by the value of the portfolio. This shows that inflation is coming down a little but is still high. We really need to boost our rate of return relative to inflation in order to retire and maintain the real value of the portfolio. It is hard to think about retiring until in inflation is more under control.

Investment income accounts for superannuation taxes, but assumes that the only tax on investments outside superannuation is exactly equal to the franking credits paid.* In retirement, the superannuation tax would go away, but there would be capital gains and other taxes on investments outside superannuation. So, probably it is in the ballpark.

* This is because the series is computed as the change in net worth minus saving and inheritances. Saving is computed after tax including superannuation contribution taxes and income tax.


Saturday, January 20, 2024

When Was the Boiling Point?

Interesting post from Enough Wealth on the "boiling point" when more of your gain in net worth comes from investment returns rather than saving. Rather than just look at the change in net worth, I created the following graph of monthly total saving from non-investment income:


This includes superannuation contributions and mortgage principal payments but not inheritances. I fitted a linear trend to this. Then I created a graph of investment income (including superannuation returns and changes in the value of our house):

 

I fitted a quadratic trend to this data. When the two curves cross we are at the boiling point. Because of the volatility of investment income it's a bit hard to see where that is. So, I also did this close up:

 

The boiling point was in January 2012 according to this analysis. Currently the trend is at about $35k per month, which is about four to five times the savings trend. That doesn't really say anything about the ability to retire. Some of the investment return is needed to maintain the real after inflation value of the portfolio and it needs to be compared to spending not saving!



Sunday, August 06, 2023

Superannuation Returns in the Long-Run

Following up from my post on how our SMSF is performing compared to our managed superannuation funds, here is how our superannuation in general has done over time:

Note that the y-axis is a log scale! Our superannuation has outperformed the MSCI index in AUD terms in the long-run. The big win was in the couple of years after 2002 when I rolled over my Unisuper fund to Colonial First State and invested in geared funds. Then I got too conservative leading up to the GFC - the flat top you can see on the red line. Superannuation returns crashed in the GFC because I got aggressive again too early. After that, we have followed the market more closely until after 2018 when we have gone into a bit more of a capital preservation mode again. This reduced the volatility in 2022 but returns in 2023 are a bit disappointing so far.

On the other hand, our non-superannuation assets had catastrophic performance up to 2009. After that, I got my act together, which eventually gave me the confidence to set up an SMSF. But you can see the value of handing control to an external manager early on.

Superannuation returns are pre-tax but after fees. My method of imputing tax paid for public superannuation funds probably exaggerates their performance a bit. These time based returns are quite different from dollar based returns. All the early volatility wasn't that important because total assets were small. Performing well now is much more important.

Enough Wealth followed up on my original post by comparing his SMSF over a longer period to a basket of industry funds.

Friday, October 14, 2022

Performance of Average Investors

 Latest version of the famous J.P. Morgan graph:

They estimate the returns for "average investors" from mutual fund flows. My return for this period was 6.12% (USD return). It's good that I am way ahead of the average investor but not good that I am behind a 60/40 portfolio (with no fees).

For a while now, I have been tracking these 20 year returns. Here is a graph with rolling 20 year USD returns for my portfolio and some key indices:

Each datapoint is the return for the 20 years up to that month. I started investing in 1996 and so the first observation is for September 2016. While I used to be worse than the median hedge fund, in the last couple of years my 20 year track record is a little bit better than the hedge fund index. I like to think it is more important to perform well the more money you have to invest :) In other words, dollar-weighted returns are more important than time-weighted returns.



Thursday, December 02, 2021

November 2021 Report

The MSCI World Index fell by 2.38%, the S&P 500 by 0.69%, and the ASX 200 by 0.37%. All these are total returns including dividends. The Australian Dollar fell from USD 0.7518 to USD 0.7122 boosting Australian Dollar returns and making USD returns very negative. We gained 1.52% in Australian Dollar terms or lost 3.83% in US Dollar terms. The target portfolio gained 2.15% in Australian Dollar terms and the HFRI hedge fund index is expected to fall 0.99% in US Dollar terms. So, we under-performed the target portfolio benchmark, the two international indices, and the HFRI but outperformed the Australian index.

The record-breaking run of winning months in Australian Dollar (and currency neutral) terms continued. We haven't had a losing month since March 2020. This is a 20 months run so far. We have had several US Dollar losses in that time. This month was the 6th and worst decline. This graph shows returns since 2018 in Australian Dollar terms:

As designed we are getting less volatility on average than the MSCI index in Australian Dollar terms. This month it was up though the index was down in US Dollar terms. If you are wondering why the scale is so wide on this graph, this is the reason:

US Dollar returns are much more volatile. For Australians, holding foreign assets reduces volatility in Australian Dollar terms as the Australian Dollar tends to move with stock prices, raising the Australian Dollar value of foreign assets when stock markets decline. For Americans, holding foreign assets increases volatility... You really would need to short the US Dollar to get similar results in US Dollar terms.

Here is a report on the performance of investments by asset class (currency neutral returns):

Gold had the best performance and contributed the most to the account followed by large cap Australian stocks.

Things that worked well this month:
  • Gold was the star performer. Gold started the month very strongly but then collapsed after Jay Powell was appointed for another term as Federal Reserve chair. But it then ended the month a lot ahead. We gained AUD 31k. In fact the US Dollar price of gold fell slightly but the fall in the Australian Dollar provided all the gains as we hold our gold as PMGOLD.AX. Runners up were Fortescue (FMG.AX) at AUD 12k and Regal Funds (RF1.AX) AUD 10k. The Fortescue position is relatively small. It gained 15%.
What really didn't work:

The investment performance statistics for the last five years are: 

The first two rows are our unadjusted performance numbers in US and Australian Dollar terms. The following four lines compare performance against each of the three indices over the last 60 months. We show the desired asymmetric capture and positive alpha against the ASX200 index. We are a little bit worse than the median hedge fund levered 1.6 times. 

We moved a little bit away from our desired long-run asset allocation. Private equity is the most underweight asset class and real assets the most overweight. Our actual allocation currently looks like this:


Roughly two thirds of our portfolio is in what are often considered to be alternative assets: real estate, art, hedge funds, private equity, gold, and futures. We receive employer contributions to superannuation every two weeks. In addition we made the following investment moves this month:

  • I closed the small positions we had in Pengana Capital (PCG.AX) following the distribution in specie from PE1.AX and sold 10k shares of PE1 I recently bought when the stock price was below NAV.
  • I bought back 4k shares of RICA.L that I sold to participate in the RF1.AX rights issue.
  • I bought 36k Regal Funds (RF1.AX) shares when they announced a jump in NAV to the share price on the hope of the premium to NAV coming back. I don't plan to hold this for the long term. I've already sold 17k of them.
  • Cadence Opportunities IPO-ed (CDO.AX). I moved the shares into Moominmama's Interactive Brokers account and planned to sell stuff there to pay down some of my CommSec margin loan. I try to keep a balance of contributions in her IB account to match money we deposited there from the mortgage redraw.
  • Planning for that move, I sold 12k MOT.AX shares, an Australian private credit fund.
  • But then WCM Global Long-Short (WLS.AX) announced that they have redone their accounts and now the post-tax NAV is the same as the pre-tax NAV, which is also higher. I thought it was a good opportunity to increase our holding in that fund to around a 2% position and bought 44k shares, which used up the cash in the account...
  • But I did sell all our holdings of Scorpio Tankers (SBBA) and most of our Ready Capital (RCB) baby bonds in her account and bought AUD 65k helping increase our holdings of Australian Dollars and reducing US Dollars.
  • I also sold our position (4k shares) in Argo Investments (ARG.AX), which was suggested by the investment review.
  • In order to hedge some remaining foreign currency exposure and get back closer to a 50/50 Australian Dollar/Foreign Currency exposure balance, I bought one Australian Dollar futures contract.



    Saturday, August 14, 2021

    Top Baggers

    Meb Faber refers to the total gain on an investment over time in terms of "baggers". If you invested $1,000 and made $9,000 then that is a 10-bagger.

    I was wondering what my best investment measured this way was. I previously calculated this using internal rate of return. But it is easier to get a high IRR on an investment held for a short time than one held for the long term. Which of my investments gained the most over time?

    If you invest $1,000 and now have $1,000 of profit it is easy to see that this is a 2-bagger. This is the way venture capital firms typical report the value relative to what they put in. But what if you added more to the investment over time? What if you sold out for a while and then bought back? Or traded in other ways?

    I realized we could get an approximation in these cases using the following pseudo-formula in Excel:

    Bags = (1+IRR)^(COUNT(X:Y)/12)

    IRR is the internal rate of return I already have. The count formula counts how many cells have an entry in them. I created a column with the following formula in it:

    =IF(Z=0,"",1)

    where Z are cells with the number of shares held each month. It returns a blank if the number is zero. We then apply the previous formula to this column (i.e. the range X:Y). 

    I've now applied this to all my currently held investments. The median investment is 1.42 (gold). The worst is 0.80 (PSTH) and the best is CFS Developing Companies at 9.69. I think my best ever investment is Colonial/Commonwealth Bank which scores 13.01. I bought Colonial shares at the demutualization. I haven't computed this for all past investments yet. Gold is also my current median investment by IRR (12.4%).

    So here are the top ten current investments using "bags", IRR, and total AUD gain :

    There is some overlap between the columns. Regal Funds and Pershing Square show up in all three. The IRR column though highlights several recent investments that have done well like WCM Global Long-Short (WLS.AX) and WAM Strategic Value (WAR.AX). The top two in the last column are our two superannuation funds that also appear in the bags column and have a lot invested in them.



    Wednesday, February 03, 2021

    Why a Constant Risk Trading Strategy Works

    A constant risk trading strategy in the day-trading context is where your maximum loss possible is a constant. There are other definitions in trend-following etc contexts where you choose a position size so that the typical or expected daily movement up or down is a constant over time and markets.

    Using the first definition, once you choose a stop loss, you compute the loss per contract or share if the stop was triggered and divide the fixed maximum loss figure by that to find out how many contracts or shares to buy. For example, if you are willing to risk $2000 on a trade and a contract will lose $1000 in the worst case, you buy (or sell) two contracts. 

    The reason this works is the maximum downside loss is capped but by trading more contracts when possible the upside is increased. This helps create asymmetry. 

    This graph shows possible loss on the x-axis and trading results (in backtest) on the y-axis, when trading one SPI contract over the last 13 months:

    And this is what happens to the returns when the maximum loss is set at the average $2,300 (yes the stop loss can occasionally be exceeded when the opening price of the day is above the entry stop):

     

    This has a lower information ratio (similar to Sharpe ratio but without deducting the risk free rate) than the one contract strategy though. It misses out on really big gains when volatility is high. But if you combine the two and set a minimum maximum loss at $2,300 you get better results than either strategy alone. Below $2,300 potential loss you trade a variable number of contracts and above it one contract only:

    This has a higher information ratio than either simple strategy but it does take on a lot more risk at times than the constant risk strategy, which for a small account trading full size futures contracts could mean just not trading when volatility is high.




    Wednesday, August 26, 2020

    What is my Best Investment?

    I was just listening to a pod-cast where the host asked the guest (Karsten Jeske) what their best investment was and they could give an answer in annual percentage terms. Up to now, I have tracked returns of individual investments in absolute dollar terms. I can easily say which has been my best and my worst on that basis. The best was the Colonial First State Geared Share Fund and the worst has been the Tribeca Global Resources Fund. But dollar returns depend on the amount invested. I do have average monthly percentage returns for many investments, but properly taking into account transactions is hard. So, I thought that I could compute the internal rate of return. This does take all transactions properly into account. You need to compute each monthly net cashflow into the investment (which I already have in individual spreadsheets I keep on each investment) and then for the current month assume that the investment is sold at the current price. Excel has an IRR function that can be applied to the column of cashflows.

    I plan to do this slowly as I have invested in around 200 different things. The first three I did are gold (34% p.a.), China Fund (14% p.a.), and 3i (6% p.a.). 3i was surprising as this is a lot less than the average annualized monthly return of almost 14%, that I previously computed.


    Monday, January 27, 2020

    Why Not Just Invest in Stock Index Funds?

    Financial Independence recently asked in the comments why I don't just invest in a portfolio of stock index funds. I answered that I am more interested in protecting against the downside now than getting richer. But basically I think you can do better than that. This is the simulated performance of our target portfolio against the MSCI All Country World Index and ASX200 in Australian Dollar terms:

    Notice what happened during the 2000-2002 Tech Wreck and 2007-2009 Global Financial Crisis? The target portfolio more or less flatlined, while Australian shares dropped 40% in 2007-9 and the MSCI fell around 20% in AUD terms. Over this whole period the portfolio also outperformed the MSCI index, though not in recent years.

    Sunday, December 29, 2019

    The Best Portfolio for Australia

    The portfolio charts website, I wrote about before, now lets you do analysis using Australian assets, inflation etc! It turns out that the best portfolio for Australia isn't the same as the best for the US... The following table shows the average and standard deviation of real returns, the maximum drawdown, and the safe and permanent withdrawal rates (preserves capital) for a 30 year retirement horizon:

    This is based on data since 1970. Based on the permanent withdrawal rate the Ivy Portfolio developed by Meb Faber is best. The 100% Aussie stocks portfolio (TSM) has a slightly higher return, but the lowest permanent withdrawal rate. So, I think Aussie investors should start to think about portfolio design from something similar to the Ivy Portfolio. It's no surprise that I have been a fan of Meb Faber and endowment style portfolios...

    Using ETFs, this portfolio recommends putting 20% into each of Australian stocks, international stocks, intermediate term bonds, commodities, and REITs.

    Using the build your own portfolio tool you can see what tweaking this beginning portfolio can do. For example, replacing half the commodities allocation with gold and half the bond allocation with extra international stocks, increases the return to 6.1% and the SWR and PWR to 5.2% and 4.4% with almost no increase in drawdowns.

    Going to 60% stocks divided equally between Australia and the rest of the world and 10% in each of bonds, gold, commodities, and REITs, is actually quite similar in return profile to the Ivy Portfolio. The key thing is to hedge Australian stocks with international and real assets. This latter portfolio is probably going to tbe basis of my own new target portfolio.


    Sunday, August 04, 2019

    Designing a Portfolio for Baby Moomin

    I decided that the best provider of investment bonds is Generation Life. This is mainly because they seem to be scandal free, not about to be sold off to an overseas manager, and have lower fees than other providers. Next I needed to pick an investment portfolio from their investment options. I decided on the following rules and criteria:
    1. 50/50 equities/fixed income and alternatives
    2. 50/50 passive and active management
    3. 50/50 Australian and international assets
    4. Pick the best fund from alternatives in each of these niches - focusing on long-term "alpha" and in particular their performance during the Global Financial Crisis and the recent December 2018 mini-crash.
    This is the resulting portfolio:

    50% Dimensional World Allocation 50/50 Trust. Here I compared a Vanguard balanced fund with this fund. In the long run, DFA have done much better than Vanguard:
    Here, Portfolio 1 is a DFA stock fund and Portfolio 3 the Vanguard equivalent. The equity curves are for someone withdrawing 5% per year in retirement. Portfolio 2 is a DFA 60/40 stock/bond portfolio. The difference is stunning. Recently, DFA hasn't done as well as value stocks are out of favor. I am betting on them coming back. If there is a major market correction we might shift this core holding to a more aggressively equity focused fund.

    10% Ellerston Australian Market Neutral Fund. Ellerston has done horribly in the past year, but prior to that it did very well for a market neutral fund. It now seems to be rebounding. This fund manager originally managed James Packer's money and then branched out.

    10% Magellan Global Fund. This has been one of the best Australia based international equity funds. It did particularly well during the GFC.

    10% Magellan Infrastructure Fund. This fund seems better than the other real estate options. It didn't do very well during the GFC, but all the others were worse.

    10% Generation Life Tax Effective Australian Share Fund. This fund is managed by Redpoint Investments. The idea is to tilt a bit towards tax effective Australian shares given the high taxes on this investment bond overall. The manager is pretty much an index hugger, but the other options for actively managed Australian shares seem worse.

    5% PIMCO Global Bond Fund. PIMCO is the gold standard for actively managed bonds. I decided to split my allocation to PIMCO between international bonds and

    5% PIMCO Australian Bond Fund, as Australian bonds have actually done very well recently.

    Friday, May 17, 2019

    Monday's Move in Bitcoin was a Huge Outlier

    The weekend move in Bitcoin extended into Monday's trading and Bitcoin ended up rising 25%. You can see how much of an outlier that was on my daily trading return vs. volatility graph:




    Since then, Bitcoin has gone into another consolidation range. This morning it looked like we might get stopped out of the long trade at the open, but the market bounced and we are still long from 5285.

    P.S. 12:55pm
    We just closed the long position and went short at 7715. Profit on the trade was USD 12.1k Of course, all this was done automatically via stop orders. 20 minutes later the short is up USD 5k. This is crazy price action.


    Wednesday, May 08, 2019

    More Asymmetry

    A couple of days ago I posted about the asymmetry of market returns capture by the target portfolio. The portfolio captured less than 100% of the upside in the markets but almost none of the downside. The chart below, inspired by a recent paper from AQR, shows the Bitcoin trading model's daily returns compared to the absolute percentage change in the price of Bitcoin futures for that day:


    The rising diagonal line are all the days when the model was properly aligned with market direction. The descending diagonal line are all the days where it was incorrectly aligned with market direction. The remaining cloud of points is where the model changed direction. Some of those days were winners and some very bad losers when the model ended up incorrectly with the market in both directions that day. For example, it was stopped out of a long position and entered a short and then the market rose for the rest of the day...

    The fitted quadratic curve shows that for low absolute price changes up or down in the price of Bitcoin, the model tends to lose money. This is because of "whipsaw". There is a strong asymmetry in the response for large moves and so the fitted curve shows that the model captures increasingly more of the return the larger the move.

    The results do conform to AQR's argument that returns to trend-following have been poor recently because markets haven't been moving enough.

    Tuesday, May 07, 2019

    Varying Position Size Still Doesn't Make Sense

    Last year, I posted that increasing trading position size when volatility is lower didn't make sense for my trading system. When the volatility was low trades tended to lose more and win less. So, trading bigger because risk was supposedly lower didn't pay off.

    Now I am using a more traditional trading system that wins by letting winners run and cutting losses short, without pretending to predict the direction of the market. Here, I have found that there is no correlation between the profit from trades and the maximum loss possible given the initial stop loss:


    The chart shows all the trades in Bitcoin futures my system would have made in the last year The x-axis shows the maximum loss on the trade of one contract (assuming we can exit at the stop loss, i.e. no Black Swans). The y-axis shows the profit for the trade. There is a slightly positive correlation, though it is not statistically significant. On the other hand, you can see that realized losses do increase with increased initial risk. The system won 46% of the time with the average win 4.1 times bigger than the average loss. The average trade lasted 5 days.

    If you adjust position size so that the initial risk of each trade is the same, returns do increase, but so does the maximum drawdown. If you scale back the average size of trades so that the maximum drawdown in percentage terms is the same as for trading with the same number of contracts each time, then returns turn out to be very similar for both strategies.

    Bottom line is that varying position size increases returns but also drawdowns by a similar amount. If you care about drawdowns it doesn't help. So, I think I will focus on controlling drawdowns when choosing position size rather than equalizing initial risk.

    Sunday, May 05, 2019

    Target Portfolio vs. the MSCI World Index

    The graph shows monthly returns for the target portfolio vs. the MSCI World Index in Australian Dollar terms. The linear fit shows a beta of about 0.3 – if the market rises 1% more , the portfolio tends to rise 0.3%. Alpha is at around 8% per year. The orange line is a quadratic fit. This suggests that beta increases, the more the market rises, while for large down moves beta is zero. This is the kind of asymmetric relationship you want to get.