Equity Allocation Calculation

nirish

I've come across this equation on Seeking Alpha to assist with equity allocation in various market conditions.  

Equity allocation = Expected return -Cash rate / Standard deviation ^2

If we just plug in the long-run return of VTI going back to inception, we get an expected return of 7.9%. The Fed is likely to hike cash rates to 5.25% this month, and the VIX is about 20. Therefore, we get an excess return of 2.6% and a standard deviation squared of 4. 2.6/4= 65%

However for me using Vanguard Global All Cap I get (7.9-5 / 0.14^2)=148%

Can anyone savier than me workout what I'm doing wrong here as I love the concept of guidance in reducing equity exposure.

numbersrule

Hi Nirish
Very interesting.  
You say you have taken VTI since inception as 7.9%, but please confirm what you believe the inception date to be.
As that time period is the basis of your analysis, you would need to take the cash rate average over the same time frame.
Needless to say you also need to take the Standard Deviation over the same time frame.
Keep in mind that all volatility calculations have to relate to a specific time period.
Please send a link to the Seeking Alpha article, because I also suspect you may need to be careful where the brackets sit in the formula.

masonic

The long term historic return of VTI is likely to be a poor substitute for the expected return of equities under a particular set of market conditions. Vanguard produces its own estimates of 10 year forward returns that could be used instead.

nirish

https://seekingalpha.com/article/4586132-sell-stocks-go-to-cash-before-recession

The VTI calculation above is direct from the article.  I understood 7.9% to be the lifetime average performance but cash rate is what is available today eg BOE base rate? 

Also I don't understand for sure how the standard deviation is calculated.  If it is 14% is the calculation 0.14x0.14 ???

numbersrule

nirish said:

https://seekingalpha.com/article/4586132-sell-stocks-go-to-cash-before-recession

The VTI calculation above is direct from the article.  I understood 7.9% to be the lifetime average performance but cash rate is what is available today eg BOE base rate? 

Also I don't understand for sure how the standard deviation is calculated.  If it is 14% is the calculation 0.14x0.14 ???

The formula needs all the elements to be in the same units.  It's a simple division to give a ratio.  In your example I believe it should read (7.9 minus 5) / 14 = 0.21 or 21%.
Equally, (0.079 minus 0.05) / 0.14 gives the same outcome.  Where or if the expected return approaches the cash rate, then the ratio approaches zero.

numbersrule

masonic said:

The long term historic return of VTI is likely to be a poor substitute for the expected return of equities under a particular set of market conditions. Vanguard produces its own estimates of 10 year forward returns that could be used instead.

Yes, I suppose the expected return depends on how distant your horizon is.
Nirish might have a few years ahead of him!

numbersrule

Hi Nirish
I can't see the article without subscribing to Seeking Alpha.
It seems to me SD would be more effective than SD squared.

nirish

Thanks for your input, that appears to give a sensible output.

My understanding of the standard deviation^2 is still lacking though.  You've divided by 14 which is the standard devation of Vanguard Global All Cap, not the squared value as per the formula?

In their example they quote VIX at 20 and then use 4 ???

If 21% is the current value it suggest I need to significantly move out of equities, currently 70% !!!

masonic

numbersrule said:

masonic said:

The long term historic return of VTI is likely to be a poor substitute for the expected return of equities under a particular set of market conditions. Vanguard produces its own estimates of 10 year forward returns that could be used instead.

Yes, I suppose the expected return depends on how distant your horizon is.
Nirish might have a few years ahead of him!

As a market timing model, investment horizon is probably only of relevance when it is very short and you should be mostly in cash anyway. Assuming you have an appropriate horizon to be in equities in the first place, then this formula seems to exist to reduce equities over the short term to avoid periods of poor equity returns. If one was to believe in it, it could be used by someone with decades ahead of them, but basing it on returns from decades of past performance seems odd. If you can model future returns, then that ought to improve the formula.

JohnWinder

‘However for me using Vanguard Global All Cap I get (7.9-5 / 0.14^2)=148%

Can anyone savier than me workout what I'm doing wrong here as I love the concept of guidance in reducing equity exposure.’ .

Easy, it’s not 7.5-5, it’s 7.9%-5%. 

Thanks for the link to the formula. There is no explanation about how the formula was developed, how it’s been tested or any validation of it. Have you followed up the link to an earlier use of the formula, and can you tell us what you’ve found to give the formula some credibility? 

The formula has ‘standard deviation’ squared which is a measure based on history. He seems to use the VIX index which is a market anticipation of volatility, expressed as a percentage although the index is not a percentage.

How much, %/year, should we expect our portfolios to outperform a ‘buy and hold’ approach, and what might be the variation in that outperformance if we use his formula? There might be costs associated with his approach: trading costs, buy/sell spreads, capital gains tax etc; we’d want it to be worth the costs.

If it worked well enough there’d be fund managers using it, you would imagine, enabling them to offer guaranteed outperformance compared with ‘buy and hold’. Anyone offering that?

You may have sensed I’m sceptical.

masonic

JohnWinder said:

How much, %/year, should we expect our portfolios to outperform a ‘buy and hold’ approach, and what might be the variation in that outperformance if we use his formula? There might be costs associated with his approach: trading costs, buy/sell spreads, capital gains tax etc; we’d want it to be worth the costs

We could do a quick back-test...

3rd Jan 2020: VIX @ 14, risk free rate at 2% (10 year Treasury yield). Excess return = 5.9%, stddev^2 = 2.

5.9/2 = 295%, which is the recommended amount to put into equities. Let's round down to 100%

Buy $10,000 S&P500 @ 3235 = 309 units

20th Mar 2020: VIX @ 66, risk free rate at 0.6. Excess return = 7.3%, stddev^2 = 44

7.3/44 = 17%, which is the recommended amount to put into equities.

Sell 256 units @ 2305 = $5900 (-$2381)

Hold 53 units worth $1222

5th Jun 2020: VIX @ 25, risk free rate at 1.5%. Excess return =  6.4%, stddev^2 = 6.25

6.4/6.25 = 102%, which is the recommended amount to put into equities... 100%

Buy $5900 S&P500 @ 3194 = 185 units

Now holding 238 units instead of the original 309

Oh yea of little faith!

Edit: appreciate I used the long term return of VTI in the calcs, but S&P500 for the trades for ease of looking up figures. I probably should have used the long term return of the S&P500 @ 9% (1996-2022), which would have made the numbers slightly more ridiculous.