## Thursday, April 29, 2010

### Problem sum

This morning, I was trying to settle a problem related to the market. In real life, much of the challenge lies in defining the problem, rather than solving it. Once the problem is defined clearly, the solution can be found, or you can find people who can help you solve your problem. I shall spend some time defining the problem.

The problem is laid out here. I had bought shares of ARA on three separate occasions. They declared a dividend of \$0.025 per share and thereafter a 1 for 5 bonus share issue (meaning that for every 5 shares held, you'll get 1 bonus share). The bonus shares are not entitled to the dividend because it comes after the dividend is declared. The last closing price of ARA yesterday before it went XA (ex-all) was \$1.15. So, the question is, what should the theoretical price of ARA shares be, after it goes XA today? The theoretical price is the price of the new ARA shares after XA, such that the gain/loss before XA but after XD (ex-dividend) is the same as the gains/losses after XA. To put it more simply, what is the price of ARA today upon XA, such that my gain/loss is the same as my gain/loss yesterday, before XA?

 A good problem will generate sparks in your neurons

I had worked out the answer, but I thought it'll be a nice exercise for those interested to solve this mathematical problem sum related to the stock market. I'll share the answers that I had worked out in a few days to give time for people interested to work it out :)

Anonymous said...

Hi LP,

I always try to use "cheapskate" aka, fast method.

1.15 -0.025 =1.125

my 5 lots = 1.125x5 = \$5.625 now become 6 lots. 5.626/6 = 0.9375

cheers,
hh

Anonymous said...

Oh dear, sorry LP, I didn't know not supposed to reveal. I have checked, 0.98 in the morning, arbitrage would bring it down to close to theoretical price.

Createwealth8888 said...

Price movement after XD, XB, XA, or X? depends on madness of men at that time.

'I can calculate the movement of the stars, but not the madness of men.' - Isaac Newton

Even great mathematician like Sir Isaac Newton couldn't solve it.

Anonymous said...

ya right :) wrong choice of word -- "arbitrage" not v. likely in this case. Price usually trade close to theoretical ex price for a very short while, thereafter, mkt forces take over.

HSBC hkd33 day before ex, 5 rights for 12 shares @hdk28 was a gd example.

Cheers to "unsolvable"!
hh

la papillion said...

Hi HH,

Haha, you're fast calculation is the same as mine initially :) But I realised it doesn't tally. I'm losing money if the price is 0.9375, so the theoretical shld be higher :)

It's okay to show everyone, there's really nothing to arbitrage anyway :)

la papillion said...

Hi bro8888,

I'm not talking about the closing price. I'm talking about the theoretical price such that before XA and after XA, there's no difference to my profit/loss.

While nobody knows the closing price, there is definitely a theoretical price after XA.

Createwealth8888 said...

Market doesn't trade on theoretical price; otherwise nobody make money. Good mental exercise but beware of such rational reasoning slowly creeping into your market views by doing more such mental exercise. 3M of trading - Mind is one of them.

Make Money Trading Shares & Cfds said...

Really it is great post .........

cif5000 said...

la papillion, your "mistake" in the calculation is that you added the dividend (which you are not entitled to) when you sold your shares before XA.

la papillion said...

Hi cif5000,

Haha, you're right :) Technically, selling the shares would not enable me to get dividend. However, I'm just mock selling the shares to see how much my profit or loss is:)

Thanks for pointing out that error, I would have missed that 'mistake' totally, haha