For individual investors, it is most efficient to allocate up to the risk tolerance limit in the asset with the highest Sharpe ratio
It is widely known that the All Country World Index (ACWI) is an excellent and efficient portfolio, and I believe it is approaching a status of being self-evident. However, it is also a fact that discourse suggesting it is better to choose other assets rather than just ACWI alone persists (especially online).
I wanted to see if I could compare this using simple numerical examples to deepen my own conviction in choosing only ACWI. The following is an attempt to trace that.
Comparison of investment patterns based on risk tolerance
[Prerequisites]
Available funds: 20 million yen
Loss tolerance: 1 million yen (maximum allowable limit during a maximum drawdown)
ACWI: Expected return 6% / Risk 20% / SR 0.3 / Maximum loss rate 50%
Bonds: Expected return 1.5% / Risk 10% / SR 0.15 / Maximum loss rate 10%
Analysis based on numerical values
1. Elimination of 'Pattern 3' based on risk tolerance
If the upper limit of risk tolerance is set at 1 million yen, Pattern 3 (aiming for a 150,000 yen return with ACWI = 2.5 million yen investment) is excluded from the options because the maximum loss amount would be 1.25 million yen.
2. Aiming for a 120,000 yen return (Consideration of Pattern 1)
When investing in ACWI, it becomes Pattern 1, where you obtain a 120,000 yen return with an investment of 2 million yen. 18 million yen in cash remains on hand.
3. Aiming for a 150,000 yen return (Consideration of Pattern 2)
To use up the 1 million yen risk tolerance and obtain the maximum return of 150,000 yen, one must choose Pattern 2, which involves investing 10 million yen in bonds (leaving 10 million yen in cash on hand).
Comparing this to Pattern 1 (ACWI investment) with a 120,000 yen return, it can be seen that to obtain an additional 30,000 yen return, the investment amount increases by 8 million yen, and the free cash on hand decreases by 8 million yen. It can be said that the capital constraint cost for this 30,000 yen increase in return is significant.
4. Comparing the same 120,000 yen return (Pattern 1 vs. Pattern 4)
Capital efficiency: Pattern 1 (ACWI) only requires an investment of 2 million yen, whereas Pattern 4 (bonds) requires 8 million yen. Pattern 4 must expose four times the capital of Pattern 1 to the market.
Difference in cash reserves: While Pattern 1 leaves 18 million yen in cash, Pattern 4 leaves 12 million yen. By choosing Pattern 1, you can secure 6 million yen more in fixed assets that are not affected by a market crash.
Unused loss tolerance: While (1) fully utilizes the 1 million yen loss tolerance, (4) only uses 800,000 yen (leaving 200,000 yen unused). This cannot be called efficient risk-taking; it is an opportunity loss and a waste.
Conclusion: Since the risk tolerance limit is 1 million yen, the practical options are limited to (1), (2), and (4).
(2): To aim for a return of 150,000 yen, invest half of the assets (10 million yen) in bonds. Cash on hand is 10 million yen.
(4): For a return of 120,000 yen, invest 8 million yen in bonds. Cash on hand is 12 million yen.
(1): To aim for a return of 120,000 yen, invest 2 million yen in All Country (Orkan). This leaves 18 million yen in cash available to move freely.
The validity of the statement 'it is most efficient to allocate up to the limit of one's risk tolerance to the asset with the highest Sharpe ratio' is summarized by this 'difference in cash flexibility'.
When these are lined up numerically, one reaches the conclusion that choosing (1)—which fully utilizes the loss tolerance limit with the smallest investment amount (2 million yen) and maximizes cash on hand (18 million yen)—is the most rational approach both mathematically and practically.
To be more precise, it means that investing in All Country within the scope of one's risk tolerance and holding the rest in cash is the most efficient method. What individual investors struggle with is ultimately which assets to invest in and how much.
The answer is simple.
Which asset: All Country (Orkan)
How much to invest: Up to the limit of your risk tolerance in All Country.
The rest: Cash (guaranteed no market crash risk)
<There is no better answer than choosing All Country as your sole investment asset and adjusting your risk through the amount invested in it. This post merely expresses these concepts using fables, rhetoric, metaphors, and allegories. Even if you get lost in the maze of choosing assets or products, the only exit is to choose All Country and adjust your investment amount.>
