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Need help with the math

By rocketjoe79 following x   2012 May 16, 1:01am 3,365 views   6 comments   watch   sfw   quote     share    


My son tells me to buy into stocks using the following scheme: if the market drops 5%, put 5% of your portfolio into the market. Likewise, I guess when the market rises, I should sell. This would be using my Vanguard 401k account, which has a limited range of investment vehicles. This is a basic buy low, sell hi, strategy I guess.

Does this strategy work? I'd like to model this using a pure sine wave function. In other words, the market fluctuates with an index starting at 5000, rising to 7500, and dropping back down to through 5000 to 2500, and begins rising again. All this on a pure sine wave curve. Is there a net gain?

Can someone help me put a function in a spreadsheet to model this performance, or point me to a site that can help? I'm no excel expert.

Let's ignore transaction costs or dividends, keep it simple for now.

1   clambo   ignore (4)   2012 May 16, 3:54am   ↑ like (0)   ↓ dislike (0)   quote   flag        

Anyone who does as you suggest is a complete fool.

2   FortWayne   ignore (2)   2012 May 16, 6:05am   ↑ like (0)   ↓ dislike (0)   quote   flag        

It doesn't work like that. You can probably buy into some mutual funds that are spread wildly enough to look like the market... otherwise you are going into individual stocks which don't track the overall market.

What your son is kind of getting at is pairing losses. And obviously look at company cash flows, it's the best way to tell if they are financially strong or just use accounting gimmicks and are overvalued.

3   T   ignore (0)   2012 May 16, 11:37pm   ↑ like (0)   ↓ dislike (0)   quote   flag        

Buying into dips will not guarantee success. Sometimes, the company will go out of business and you won't see them on market anymore.

4   rocketjoe79   ignore (0)   2012 May 18, 4:41pm   ↑ like (0)   ↓ dislike (0)   quote   flag        

Just help with the math please, not investment advice.

5   FNWGMOBDVZXDNW   ignore (2)   2012 May 19, 4:12am   ↑ like (1)   ↓ dislike (0)   quote   flag        

Dollar cost averaging works well in this situation, because you are always buying, and you buy more shares when the price is lower. In your strategy, you will selling when the price is low on the way down and buying when the price is low on the way up. Because of this, you do not come out ahead.

I set this up in Excel, with a stock market value of 1 + 0.5 sin (2pi()x) over 1 yr (1 sin wave). If you have 1 dollar invested the whole time, your you follow your strategy, you end up with 0 % return. If you invest with your strategy, you get 0% return. If you invest based on the derivative (lower investment when the derivative is lower), then you get a return of 26%. The problem is that you cannot measure the derivative effectively with stocks.

If you do not know how to set this up in Excel, but know calculus for some reason, you can set it up as follows:

Stock market = 1 + 0.5 sin (2*pi()*t)
At t = 0, stock market = 1. At t = 1, stock market = 1 again. If you invest a fixed amount at the beginning, your gain will be 0%.

Instantaneous rate of return = derivative = 0.5*cos(2*pi()*t)

Total yearly earnings = integral of instant rate of return over year.
For fixed investment,
earnings = integral (0.5*cos(2*pi()*t)) = 0.5*sin(2*pi()*t)
After 1 year, the earnings = 0, because sin (2*pi()) = 0. After 1/4 yr, your earnings are 0.5, which is consistent with our starting assumptions.

If you change the amount invested, your daily rate of return is scaled by the amount invested, so if you invest 0.5-0.5sin(2pi()t), then you will have 0 invested at the peak of the curve, and be full in at the bottom. To calculate the earnings, you have:
integral(0.5*cos(2*pi()*t)*(0.5-0.5sin(2pi()t)) = integral (0.25*cos(2*pi()t) -0.25*cos(2*pi()*t)*sin(2*pi()*t)
The first integral is zero when done over 1 yr. The 2nd can be calculated by rewriting cosAsinA = 0.5sin(A-A)+0.5sin(2A). sin(A-A) = sin(0) = 0. So, the integral is now:
0.5*0.25*sin(4pi()*t), which is equal to zero after the full year. So, the calculus shows the same result as the numerical integration.

6   michaelsch   ignore (0)   2012 May 21, 7:06am   ↑ like (1)   ↓ dislike (0)   quote   flag        

Let’s take your example. The market is at 7500 and you got all in cash (instruments).

It goes down all the way to 2500. Any time it’s down 5% you move 5% of your total investment to buy in. Let’s say it does it every month.

So, the buying points would be:

1 at 7125
2 at 6768.75
3 at 6430.3125
4 at 6108.796875
5 at 5803.35703125
6 at 5513.1891796875
7 at 5237.529720703125
8 at 4975.65323466796875
9 at 4726.870572934570313
10 at 4490.527044287841797
11 at 4266.000692073449707
12 at 4052.700657469777222
13 at 3850.065624596288361
14 at 3657.562343366473943
15 at 3474.684226198150246
16 at 3300.950014888242734
17 at 3135.902514143830597
18 at 2979.107388436639067
19 at 2830.152019014807114
20 at 2688.644418064066758

At which point you are 100% in stocks.

You would like to also buy twice more:

21 at 2554.21219716086342
22 at 2426.501587302820249

But you have no cash for it. So last two month of the bear market you just stay with stocks loosing their value.

Now let’s say it turns to bull market. It again rises 5% every month. It will take now 24 month to go back above 7500. According to your rule you should start selling now.

The market will go up like this:

1 at 2547.826666667961261
2 at 2675.218000001359324
3 at 2808.97890000142729
4 at 2949.427845001498655
5 at 3096.899237251573588
6 at 3251.744199114152267
7 at 3414.33140906985988
8 at 3585.047979523352874
9 at 3764.300378499520518
10 at 3952.515397424496544
11 at 4150.141167295721371
12 at 4357.64822566050744
13 at 4575.530636943532812
14 at 4804.307168790709453
15 at 5044.522527230244926
16 at 5296.748653591757172
17 at 5561.586086271345031
18 at 5839.665390584912283
19 at 6131.648660114157897
20 at 6438.231093119865792
21 at 6760.142647775859082
22 at 7098.149780164652036
23 at 7453.057269172884638
24 at 7825.71013263152887

But based on your rule you would be able to sell only 20 times.
So, you made 20 sales and 20 purchases and if you sort your sales and purchases by the price you’ll see that on each level you’ve sold for less than you’ve bought.

The bottom line: you’ve lost money plus you’ve lost interest on the fixed income investment.

Why did it happen? In our example your strategy caused you missing the bottom on the buying and missing the top on selling.
Is it avoidable? Probably yes, you could spend less than 5% every time the market falls 5%. But the problem is that in real life that would cause you keeping only tiny portion of you funds in stocks. That means you are practically all invested in fix income with a small interest.





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