Few Important Mathematical Concept in Investing



Stumbling upon this blog post from one of the famous Financial Blogger from HKG (取之有道)

Other than the famous “Rule of 72” which is well known by most of value investors , below are few more mathematical concept which I think is also rather important for anyone who is involving in stock investing.



Concept explained : Rule of 72 ( by Investopedia )

The 'Rule of 72' is a simplified way to determine how long an investment will take to double, given a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors can get a rough estimate of how many years it will take for the initial investment to duplicate itself.




For example, the rule of 72 states that $1 invested at 10% would take 7.2 years ((72/10) = 7.2) to turn into $2. In reality, a 10% investment will take 7.3 years to double ((1.10^7.3 = 2).


When dealing with low rates of return, the Rule of 72 is fairly accurate. This chart compares the numbers given by the rule of 72 and the actual number of years it takes an investment to double.


Rate of Return
Rule of 72
Actual # of Years
Difference (#) of Years
2%
36.0
35
1.0
3%
24.0
23.45
0.6
5%
14.4
14.21
0.2
7%
10.3
10.24
0.0
9%
8.0
8.04
0.0
12%
6.0
6.12
0.1
25%
2.9
3.11
0.2
50%
1.4
1.71
0.3
72%
1.0
1.28
0.3
100%
0.7
1
0.3


Notice that, although it gives a quick rough estimate, the rule of 72 gets less precise as rates of return become higher. Therefore, when dealing with higher rates, it's best to calculate the precise number of years algebraically by means of the future value formula.


I loosely translate it to English in ()  

1        1)    一支股票跌了一半之後,需要升一倍才重返原來價位。
( A stock which has dropped by 50% will require 100 % gain eventually to return to original price. )

2) 一支股票將會跌九成的話,你在它跌去八成時買入,你還將會損失一半。
( If a stock is expected to dropped by -90% , you bought in at -80% , you still will loss by half of your value.)

3) 每年12%回報,1年是1.1210年後是三倍多,20年後近10倍回報。
( At 12% return p.a , 1 year return is 1.12 , after 10 years will be more than 3 times , after 20 years will have almost 10 times return.)

4) 每次交易失去2%(交易成本?),10次後只剩下八成本金,20次後只餘下三份之二。
(Your transaction cost is 2% in every trade , after 10 times of trading  you will left will 80% of capital , after 20 times , will left will 2/3 of capital.)

5) 定止蝕位在10%,止蝕5次本金只剩下六成,止蝕十次只剩下三成多。
( Fixing your cut loss at 10% , 5 times cutting loss will left you with 60% of capital , cut loss of 10 times will only left 30% of capital .)




6) 一次止賺10%,一次止蝕10%,出來的結果是本金的0.99,而不是打和,即少於1

( One time profit taking of 10%, One time cut loss of 10% , resulting with 0.99 time of capital , not balance up but with less than 1.)

7) 一次止賺30%,一次止蝕30%,出來的結果是本金的0.91
( One time profit taking of 30% follow by one time 30% cut loss , result with be remaining capital of 91 % or 0.91 )


You may read the full blog post in below link : ( In Chinese )


For more article on this blog 取之有道 ) Please refer to my blog list :



Another useful formula and table : 


Percentage Recovery Formula :
y = x/(1-x)

where y is the percentage gain required to break even and x is the percentage lost.
So if you lost 80% (.80), the break-even recovery gain is .8/(1-.8)=4, or 400%.





The worst performance stock ( O&G sectors )  in my portfolio is sitting with paper loss of around -30% , which will require more than 42% of return in future .

How about you ? What is the worst counter and percentage of loss in your portfolio and the require return to break even ?


Cheers !




“ The focus of most investors differs from that of value investors. Most investors are primarily oriented toward return, how much they can make and pay little attention to risk, how much they can lose. “ by Seth Klarman

Comments

  1. Hi STE,

    Quote " 一支股票跌了一半之後,需要升一倍才重返原來價位。
    ( A stock which has dropped by 50% will require 100 % gain eventually to return to original price. )"

    Unquote.

    Base on relative math, it is correct.

    However, if we base on absolute term, then it is not right. For example, if we lose $5K base on $10K capital, we lost 50%. To gain back to $10K, we need to recover 50%. In absolute term, if we gain back $5K, then we breakeven.



    ReplyDelete
    Replies
    1. Correction ...To gain back to $10K, we need to recover 100% [instead of 50%]

      Delete
  2. Hi Ray,
    Yah ! U got it ... this is base on relative term .. in absolute , $5K lost need $5k recovery / return ... that's what the carton tell us " MATH = Mental Abuse To Human " ,,, hahaha . depend on where and how we interpret it .. :)
    Cheers !

    ReplyDelete
  3. Hi STE,

    My worst counter also from O&G and it's from US.. so far it's at -80% so I already treated it as "gone case" account lol

    ReplyDelete
    Replies
    1. Hi Richard ,
      Wow! Base on above table, you need 400 % to break even from current price ..😧 well, in investing, we make mistakes and learn from time to time. ..交学费。
      Cheers!

      Delete
    2. Hi Richard ,
      Wow! Base on above table, you need 400 % to break even from current price ..😧 well, in investing, we make mistakes and learn from time to time. ..交学费。
      Cheers!

      Delete
    3. Yup! That's why I already treated it as "gone"... :-)

      Delete

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