Global Macro Trading Journal

Its not that big of a surprise that the computer would get rid of gold and favor US bonds with the additional 1879-1926 period. In that period (gold standard) bonds were a better hedge. They returned a lot more than gold and were pretty stable (no losing months). What's surprising is that the stock allocation held steady at 20%.
But this also shows the importance of building an 'all wheater' allocation instead of curve fitting things. Anyone who got rid of gold and favored bonds, in 1926, missed out on the significant advantage that gold had from 1926 to 2016 as the Great Depression hit (and the dollar was devalued) and a paper money system started to emerge. In this fiat world the value of gold as an hedge increase and its Sortino/Sharpe boosting effect was significant
 
Another answer to the question "why own gold? it doesn't pay a dividend"

This is with 1926-2016 and a 0% allocation to US bonds

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In some countries, there is no bond market with duration (no one lends money to the government for long periods due lack of trust). In that situation, risk hedges are gold (and foreign assets). Normally the computer would recommend 12% in Gold. Without access to US bonds, it found value in adding an extra 5.36% to gold.
Interestly, it still held stocks steady at around 20%, even though it didn't had access to the hedge capabilities of US 10y bonds
 
So I'm trying figure out why the computer like 20% equities so much (and it seems to be some kind of floor). I thought it might have to do with rebalancing (I'm using 1y rebalancing). So I decided to vary that and not allow the computer to buy gold or US bonds. So I'm essentially asking if what the optimal allocation between stocks and cash (bills) regardless of rebalancing

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So the computer recommends pretty much the same thing, regardless of rebalancing effects. With 1m rebalancing it recommends 71% US bills and 29% stocks

With a bonds + stock mix (no gold or bills allowed). It seems similar

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What does that mean? I guess what it means is that the 'secret' formula to create an all wheater allocation are the absolute level of volatilites among different assets. The correlations can help here and there (to create a hedge effect) but only up to a point. I'm doing all that I can to get the computer to buy more stocks but it just can't (not if the goal is maximize the Sortino ratio).
 
You would expect the computer to want to buy more stocks when it has access to US bonds, but it doesn't. It actually allocates less to it than when it can only buy bills and stocks. Why? Because it is drawn to the big Sortino that bonds have. In my sample the individual asset classes are quite different

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So the computer didn't "really cared" that when stocks fell, bonds rose or that you could buy more stocks (cheaper) when you had bills during bear markets. I put "really cared" in quotes because it did care about that to SOME extent. I mean, its going to allocate a few percentage points here and there when it notices it produces a good effect but OVERALL, for an entire portfolio Sortino ratio, what matters is how MUCH of each individual asset (and its Sortino) it puts in the 'blended mix'. While rebalancing and negative/low correlations are nice, it wont help if you have to big up TOO MUCH in Sortino "champs" like US bonds. I think that's why the computer doesn't like to get away from 20% in stocks, and it pretty much almost never goes above 30%.
 
When you allow all asset classes, the computer seems to find an equilibrium (after varying the rebalancing from 1m to 12m to 48m to 88m) at around

16-21% stocks
64-74% US bonds
8-13% gold

Sometimes it would throw some bills in there but I could easily find a similar non-bill portfolio with almost equal stats, so I could make it all comparable.

What this tells me that, preliminarly, it seems that a typical well balanced allocation seems to be

70% to High Sortino lowish return assets
20% to Not as high Sortino but high return assets
10% to Lowish Sortino but "hedge" assets with a high kurtosis/skewness (Gold type asset)
 
When I run tests on annual data the recommeded allocation was for 35-50% in equities. With monthly data the recommeded allocation was 15-25%.

So, with that monthly US data, the computer finds optimal to own 3.5 units of 10y bonds for every 1 unit of stocks with 0.5 units in gold. What if you have access to 30y bonds?

Well, thats where it gets interesting. If we assume that 30y bonds have twice the duration of 10y bonds (I'm not sure historically where that relationship has been at, if anyone know, im all ears) then one needs only 1.75 units of bonds to make it an equivalent portfolio. So the portfolio would look like
35% 30y bonds
20% stocks
10% gold

And yet, now one has 35% in free cash to invest. What if you reinvested in the same ratios?
So add
18.8% 30y bonds
10.7% stocks
5.5% gold (rounding)

So the final result is
54% 30y bonds
30.7% stocks
15.3% gold
=100%

Now, the risk is that staying on the long end of the yield curve is wrong place to be. To derive all the 'needed duration' from just one point of the curve seems dangerous. Perhaps its better to get rid of 30y bonds and buy some 10y bonds (and remove some stock and gold to compensate as they are not high Sortino assets). So one would be invested in "two" asset classes, long term duration and medium term duration. That would be more robust and it would protect against rising rates.

How much to invest in 'medium term duration'?. I'm not sure, the computer seems to find optimal a 'new asset class' at around 10-20% allocations (thats what happens to stocks and gold), at more than that it seems to balk, at less, there are benefits to increasing it, so it tends to want to increase. But medium term bonds are high sortino, so presumably one could increase at will.

But that would defeat the purposes of using 30y bonds (more capital efficient, enables boosting of returns, kinda like free leverage). So lets put 15% there and obtain that by selling 30y bonds, stocks and gold at current ratio of 54% bonds, 30.7% stocks, 15.3% gold
So
-8.1% 30y
-4.605% stocks
-2.295% gold

So the final portfolio

46% 30y Bonds
26% stocks
15% intermediate bonds
13% gold

Whats interesting is that this is remarkably close to the Dalio portfolio he gave to Tony Robbins
 
30y have slighly lower Sharpe Ratios then 10y bonds (and presumably, lower Sortino ratios) looking at 1978 to 2016 data. But it isn't all that much, about 10-12% lower Sharpe. So, they fit in with the formula of 70% in high Sortino pretty well. Especially, because they are so capital efficient. I believe that's why Dalio favored it in his recommended portfolio. I mean, one can build an almost equivalent portfolio to the 10y bond one and still have 35% in free cash to invest (or 30% or 40%, it depends on what kind of duration ratio to the 10y bond one is using).

That free cash will be invested yet more assets at the optimal allocation, which will boost returns further. The monthly compound return rate will go through the roof and when the Sortino looks at that, it likes it very much
 
But I agree with Dalio, the key is to have that 15% in intermediate (or 10% or 20%). That way the portfolio has SOME way of adjusting to a rising rate enviroment and the bond portfolio is more robust to different 'weather' conditions
 
Thats what the pundits missed when the Tony Robbins book came out and they were puzzled by the amount of 30y bonds Dalio recommended. The 'free leverage' that one gets from 30y bonds enables one to buy more stocks and bonds (after all, if you made an equivalent portfolio and now you have all the free cash, why SHOULDN"T you reinvest at the same ratios in the same asset classes?). So using 30y bonds and duration is a double portfolio booster. Not only usually you will pickup more yield (stated yield and expected long-term yield) but also you will be ABLE to own more stocks. So it boosts returns twice, with limited risk
 
So these are the formulas I was able to come up with using 1926-2016 monthly data

Optimal portfolio:

For the US:

3.5 units of 10y bonds
1 unit of stocks
0.5 unit of gold

With 2-1 30y to 10y bond duration difference

46% 30y Bonds
26% stocks
15% intermediate bonds
13% gold

How to convert this to an emerging market is more complicated. Especially given the limitation of asset classes (sometimes there is no duration or duration is a risk asset) and additional risks those countries have. That's the next part of my project
 
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