Tactical Asset Allocation Strategy - A Very Simple Approach
Team Latte
Oct 21, 2005
A fund manager, who wanted to allocate funds between the Japanese stocks and Hong Kong stocks, sat agonizing over the asset allocation problem on a recent Friday afternoon. The fund manager who had studied mathematics and statistics until his high school and thoroughly detested those two disciplines, had risen to prominence solely because he was always at the right pub at the right time. He decided to call on one of his analysts for help; this analyst was indeed a very bright guy, not because he had any fancy degrees or knew Ph.D. level math, but simply because he had the ability to analyze problems at the intuitive and heuristic level
Jonathan: "Rajeev, I have a serious problem!"
Rajeev: "Did your yacht break down? No, of course not! Let me guess¡KYou can't get a booking for your Christmas bash at Hyatt in Sydney. I'm telling you forget Sydney, try Jaipur - its beautiful."
Jonathan: "Asia B portfolio has to be invested between Japanese and Hong Kong equity and Brad wants the allocation by Monday morning. Can you work out something? I need some ammo for the Investment Committee meeting. Just an estimate¡K.,.anything will do¡Kjust see that is not a 50:50 allocation."
Rajeev: "Hey, I look at sectors and micro-strat, run it in the simulator¡Kask, Joe, he does Japan and North Asia with Barb, and Barb's pretty good with allocation models"
Jonathan: "It's not rocket science, for f's_____ sake!! Just run some numbers, do what you Indies are good at¡K.give me a number, mate. David's got my balls, and I need to take wife out tonight. Give me something sexy, you know¡K.I owe you one".
Rajeev, the brilliant analyst from India, took ten minutes and send an email to Jonathan: Japan - 78% and Hong Kong - 22%, mention 'tactical asset allocation' and 'excess return over vol' but definitely mention 'history repeats itself.' The last line was underlined in bold.
Here is what Rajeev did:
He took the monthly values of Nikkei225 index and Hang Seng Index between 1st October 2004 and 3rd October 2005 and calculated their log return using price relatives. Then he converted them into annualized return using the geometric average. He then calculated the monthly volatilities of the two indices and then annualized those volatilities to annual volatilities
Nikkei225
Annual Return (Geometric average): 22.25%
Annualized Realized Volatility: 13.44%
Hang Seng Index
Annual Return (Geometric average): 10.33%
Annualized Realized Volatility: 14.46%
He also calculated the historical correlation between the returns of these two indices for the above period. It turned out to be: 0.3805.
The above showed that based on one year history Japanese broader equity market has outperformed the Hong Kong broader equity market. Then he made an assumption that history repeats itself and therefore in the next one year the two markets will mirror their last year's performance. He knew that this assumption is totally untenable and can eventually prove fatal; but at the same time, it should more than suffice for the totally useless and futile investment committee meetings that the fund managers would have on coming Monday.
By our assumption, since Nikkei is expected to return more (and the same amount as last year) than Hang Seng a larger portion of funds should be allocated to Nikkei225. That is a no-brainer. The real question is how much more, or what exact proportion to allocate to Nikkei? And to answer this question Rajeev needed to find out what was the probability that Nikkei225 will outperform the Hang Seng?
The answer and the rest of the calculation were easy and done Karl Friedrich Gauss, the famous German mathematician, more than a century ago.
Volatility of Spread between Nikkei and Hang Seng Return: 15.55%
Excess of Nikkei Return over Hang Seng Return: 11.92%
If both returns are normally distributed then the probability of Nikkei outperforming the Hang Seng is given by the normal distribution value of the ratio of excess return over the volatility of the spread of the returns.
Therefore, the volatility of the spread is calculated as:
If we look up the ratio of 11.92% over 15.55% in the Normal distribution table or use the Excel function to calculate the cumulative probability we will get an answer of 77.84%. That is the probability that Nikkei will outperform the Hang Seng in the coming year
Therefore, 77.84% of the funds should be allocated to Nikkei (Japanese stocks) and 22.16% of the funds should be allocated to Hang Seng (Hong Kong stocks).
This technique when expanded under multi-asset scenario with slightly greater heuristic rules forms the basis of Tactical Asset Allocation models.
Disclaimer
"Risk Latte uses proprietary and non-proprietary mathematical and empirical models to measure the volatility and estimate the direction of the market. There is no guarantee of any particular outcome happening and readers must exercise caution while interpreting the conclusions of this article. Risk Latte Company is not a registered stock broker or an SFC registered entity and readers must take advise from their financial advisors, stock brokers, research analysts and bankers while making any buying or selling decisions. Risk Latte Company is not in the business of making stock or asset forecasts whether explicitly or implicitly and shall not be responsible for and/or liable for any losses arising out of any trading decisions based on the above article."
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