Maximize Compound Interest [1]

This article discusses the basic concepts and how to materialize and maximize compounding growth in the stock market.

A few days ago while I was stuck in the heavy traffic of Silicon Valley,  I listened to a financial radio program .  The host invited a real estate investor who bought a house 20 years ago.  In the last 20 years,   Silicon Valley housing market is booming. Then he started to talk about the extremely high reward of that investment, which he said it was doubled every year ! (Bad signal, I might have a bad memory). I immediately realized he must be joking and something must be wrong in his calculation. Assuming a $ 50,000 investment 20 years ago, 100 percent return per year after 20 years is: 1+100%)20 = 5×1010, which is 50 billion dollars! OMG, that lucky guy just became one of the the world’s top 10 richest man by purchasing a house, too easy! For those neophytes,  if he can follow a wise man who continuous double, after 10 or 20 years, would not be easy to become a millionaire or billionaire.

As can be seen, although the annual 100% return is not sustainable, but the use of time compounding long-term stable growth is the magic of accumulating wealth. Einstein once commented on compound rate:

“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.”

Compound interest is that you reinvest the interest you earned each year and then take tat together with the principal investment, the absolute value of the growth rate of earnings faster. Einstein also discovered the Rule of 72, which can be simply estimate how long it will take to double for a give compound interest rate, here is the formula:

Years to double = 72 / Interest Rate

 If the annual interest rate (APR) is 9%, then in the case of compound interest is calculated once a year, your investment will be doubled in eight years. You invest  of $100,000 in the first eight years will become $ 20,000, and reach $ 1,580,000 to 32 years . If the annual income is 18 percent,  you will get 20 million dollars after 32 years. 18% a year seems to be too easy, but it is not easy to maintain every year. Our goal is to achieve feasible, repeatable, scalable , low risk investment which we can maximize compound interest.

 

yr
1
2
3
6
8
12
24
32
 
 
0% $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00
1.00% $101,000.00 $102,010.00 $103,030.10 $106,152.02 $108,285.67 $112,682.50 $126,973.46 $137,494.07
2.00% $100,020.00 $104,040.00 $106,120.80 $112,616.24 $117,165.94 $126,824.18 $160,843.72 $188,454.06
3.00% $103,000.00 $106,090.00 $109,272.70 $119,405.23 $126,677.01 $142,576.09 $203,279.41 $257,508.28
4.00% $100,040.00 $108,160.00 $112,486.40 $126,531.90 $136,856.91 $160,103.22 $256,330.42 $350,805.87
6.00% $100,060.00 $112,360.00 $119,101.60 $141,851.91 $159,384.81 $201,219.65 $404,893.46 $645,338.67
8.00% $108,000.00 $116,640.00 $125,971.20 $158,687.43 $185,093.02 $251,817.01 $634,118.07 $1,173,708.30
9.00% $109,000.00 $118,810.00 $129,502.90 $167,710.01 $199,256.26 $281,266.48 $791,108.32 $1,576,332.88
12.00% $112,000.00 $125,440.00 $140,492.80 $197,382.27 $247,596.32 $389,597.60 $1,517,862.89 $3,758,172.63
18.00% $118,000.00 $139,240.00 $164,303.20 $269,955.42 $375,885.92 $728,759.26 $5,310,900.63 $19,962,927.70
24.00% $124,000.00 $153,760.00 $190,662.40 $363,521.51 $558,950.67 $1,321,478.87 $17,463,063.93 $97,609,912.89
  • Feasible:  non-professionals do not need to spend a lot of time and effort required to track more than 10 stocks, or time the market, passive or semi-passive management should be sufficient to ensure the reward. a.k.a to achieve the optimum reward on the time invested.
  • Repeatable:  That strategy can be used repeatedly, that is, when an indicator appears, according to the principles of the preset operation.
  • Scalable: The performance of the strategy won’t be worsened with escalating cost if the scale of investment is increased. For example, for securities of the low liquidity, such as certain options and small-cap stocks,  price can be go up or down drastically because we buy or sold transaction, leading to lower reward and a sharp rise of investment costs. Some strategies which is feasible when asset is $1,000,000 will become unpractical when the managed asset zoomed to   $100,000,000.
  • Low risk: return on investment is relatively stable, less ups and downs.

I would like to discuss the practical trading strategies to maximize compound rate from the aspects of  steady growth, compounding frequency, security selection, dividend reinvestment, covered calls, short puts with intent to buy, taxes & fees.

1. Steady growth. Take a look at Berkshire Hathaway, S & P 500 and 2x S & P 500’s performance in this century.

 
BRK
SPX
2xSPX
20006.50%-9.10%-18.20%
2001-6.20%-11.90%-23.80%
200210.00%-22.10%-44.20%
200321.00%28.70%57.40%
200410.50%10.90%21.80%
20056.40%4.90%9.80%
200618.40%15.80%31.60%
200711.00%5.50%11.00%
2008-9.60%-37.00%-74.00%
200919.80%26.50%53.00%
201013.40%15.10%30.20%
20114.60%2.10%4.20%
201214.40%16.00%32.00%
201318.20%32.40%64.80%
mean9.89%5.56%11.11%
Stdev0.0910.1990.398
compound rate9.51%3.60%1.64%
Investment of $100K on 1/1/2000$356,880$164,135$125,560

Buffet’s (BRK.A/BRK.B) performance of these years is not as great as his heyday, but still quite outstanding comparing to S&P. Take a look at 2xSPX (this is just an analog 2x yearly performance, real 2x daily SPX ETF performance might be more volatile). In the past 14-year period, it rose more than 30 percent six times, only decline over 30 percent twice. The arithmetic mean of 11.11%, much higher than 9.89% BRK’s. But BRK 14-year compound rate was 9.51%, total revenue is + 256.88%, while 2xSPX the compound rate is only 1.64%, the total reward is only + 25.56%, and even worse than buy & hold treasury bond. Why? The answer on the standard deviation, in these 14 years, BRK never fell more than 10% once, there was only one year it rose than 20%, the highest increase was a mere 21% (I believe lots of investors can easily beat Buffet once, but may not beat him in a long run!). BRK standard deviation is 0.091, while 2xSPX drop more than 20% for three times, standard deviation is 4 time of that of BRK! It seems the problem lies in the fall, 2xSPX decreased by 74% in 2008, then what is the percentage it can rose to break even, remember: not + 74%, but a startling + 285%! That is continuous growth in 15 years at an annual rate of 9%! So remember Buffet’s famous quote: Rule No.1: Never lose money; Rule No.2:. Never forget rule No.1!

Therefore, without influx of fund, if the investment is wiped out, it would take almost forever to recover. So what kinds of securities can be surely forfitable giving unlimited time? As long as the money can pay interest or dividend, there is always a day the interest or dividend paid will surpass the principle! There are categories of interest or dividend yield investments, the risk from low to high, are CD (Certificate of Deposit)s, treasury bills, notes and bonds, municipal bonds, cooperate bond, Real Estate Investment Trust (REIT), utility stocks, preferred stocks, Master Limited Partnership (MLP) . We will discuss the pros and cons of various investment securities in the third part of the series.

2. Compounding Frequency

An overlooked factor is the compounding frequency. Stock or fund dividends can be paid yearly, quarterly or monthly. If every time the dividend reinvest, then the next dividend payment is will be calculated based on the latest principal, which is the sum of last dividend paid and the principal of the previous period, and that is compounded growth.

We will compare the APR (Annual Percentage Rate) 4%, 6%, and 8% with monthly, quarterly, annually compounding.

compound frequency
Annually
Quarterly
Monthly
Annually
Quarterly
Monthly
Annually
Quarterly
Monthly
yr4.00%4.00%4.00%6.00%6.00%6.00%8.00%8.00%8.00%
1$100,040$104,060$106,136$100,060$1,061,364$1,061,678$108,000$108,243$108,300
2$108,160$108,286$112,649$112,360$1,126,493$1,127,160$116,640$117,166$117,289
3$112,486$112,683$112,727$119,102$1,195,618$1,196,681$125,971$126,824$127,024
6$126,532$126,973$127,074$141,852$1,429,503$1,432,044$158,687$160,844$161,350
8$136,857$137,494$137,640$159,385$1,610,324$1,614,143$185,093$188,454$189,246
12$160,103$161,223$161,478$201,220$2,043,478$2,050,751$251,817$258,707$260,339
24$256,330$259,927$260,753$404,893$4,175,804$4,205,579$634,118$669,293$677,764
32$350,806$357,385$358,899$645,339$6,724,398$6,788,405$1,173,708$1,261,310$1,282,639

As can be seen, if it is 8% APR, after 32 years, monthly compound has been higher than the yearly compound of more than 10%. Obviously, if APR is fixed, the frequency of dividend payment, the higher the ultimate benefits (higher APY). If a stock can pay dividend weekly or monthly, that will be ideal to grow compounding interest. If not, we can take advantages of covered call or diagonal spreads to enable the weekly dividend for ourselves.

 

 

 

 

 

 

 

 

 

 

 

复利的最大化-【1】

本文科普复利的基本概念和探讨如何在股市中实现复利增长。科普部分大牛可跳过。

几天前边开车边听硅谷某华语电台的财经节目。里面一位大佬谈到20年前买了一栋投资房,结果这20年硅谷房市火热,总体投资回报平均每年翻一翻!(信号不好,可能有误)。我立马趴下了。虽然书读得不多,但我还是能知道那位老大那个地方计算有误。假设20年前投资50,000元,那么按大佬所说的每年100%回报,20年后就是:$50,000 x (1+100%)20 = 5×1010,也就是500亿美金!OMG,买个黄子就能跻身世界首富前十位,太容易了!板上如果有大牛能连续double,青蛙只要跟个10年20年,岂不是轻松成为千万富翁,亿万富翁了。

可以看出虽然每年100%不可持续,但利用时间复利长期稳定的增长是积累财富的法宝。爱因斯坦是这样评论复利滴:

“复利是世界第八大奇迹。了解它,就有得赚,不了解它,就有得赔。”
“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.”

科普一下复利,就是你把每年赚的部分加上本金再拿去投资,在收益率一定的情况下,收益的绝对数值增长速度越来越快。爱因斯坦老人家还总结了72法则,即翻倍的速度是72除以百分比。如果年收益是9%,那么在每年计算一次复利的情况下,您的投资将在8年翻一翻。您投资的100,000美金,在第8年约为为$20,000,到第32年成为$1,580,000,轻松成土豪。如果年收益是18%,到32年将得到2千万美金。18%一年对于本版的大牛来讲不要太轻松,但年年保持并不容易,我们的目标是实现可操作,可复制,可规模化,低风险的前提下实现复利最大化。

yr
1
2
3
6
8
12
24
32
 
 
0% $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00
1.00% $101,000.00 $102,010.00 $103,030.10 $106,152.02 $108,285.67 $112,682.50 $126,973.46 $137,494.07
2.00% $100,020.00 $104,040.00 $106,120.80 $112,616.24 $117,165.94 $126,824.18 $160,843.72 $188,454.06
3.00% $103,000.00 $106,090.00 $109,272.70 $119,405.23 $126,677.01 $142,576.09 $203,279.41 $257,508.28
4.00% $100,040.00 $108,160.00 $112,486.40 $126,531.90 $136,856.91 $160,103.22 $256,330.42 $350,805.87
6.00% $100,060.00 $112,360.00 $119,101.60 $141,851.91 $159,384.81 $201,219.65 $404,893.46 $645,338.67
8.00% $108,000.00 $116,640.00 $125,971.20 $158,687.43 $185,093.02 $251,817.01 $634,118.07 $1,173,708.30
9.00% $109,000.00 $118,810.00 $129,502.90 $167,710.01 $199,256.26 $281,266.48 $791,108.32 $1,576,332.88
12.00% $112,000.00 $125,440.00 $140,492.80 $197,382.27 $247,596.32 $389,597.60 $1,517,862.89 $3,758,172.63
18.00% $118,000.00 $139,240.00 $164,303.20 $269,955.42 $375,885.92 $728,759.26 $5,310,900.63 $19,962,927.70
24.00% $124,000.00 $153,760.00 $190,662.40 $363,521.51 $558,950.67 $1,321,478.87 $17,463,063.93 $97,609,912.89
  • 可操作是指非专业人士不需要需花费很多时间和精力跟踪10只以上的股票,或time the market,passive或半passive 管理足矣。
  • 可复制是指可以反复使用,即当某项指标出现时,即可按预先设定的原则操作。
  • 可规模化是指在投资成本不会因为投资规模扩大很增加,例如如果大量购买流通性较差的证券,如某些期权和小盘股,就会抬高该证券的价格,导致成本急剧上升。
  • 低风险是指投资回报率比较稳定,少大起大落,不见外婆也不爆,一点不吸引眼球。

以下从稳定增长,复利频率,证券选择,dividend reinvestment, covered calls, short puts with intent to buy, tax & fee consideration  这几个方面来和大家探讨最大化复利具体操作。

1. 稳定增长。先看看Berkshire Hathaway, S&P 500 和 2x S&P 500在本世纪的表现。

 
BRK
SPX
2xSPX
20006.50%-9.10%-18.20%
2001-6.20%-11.90%-23.80%
200210.00%-22.10%-44.20%
200321.00%28.70%57.40%
200410.50%10.90%21.80%
20056.40%4.90%9.80%
200618.40%15.80%31.60%
200711.00%5.50%11.00%
2008-9.60%-37.00%-74.00%
200919.80%26.50%53.00%
201013.40%15.10%30.20%
20114.60%2.10%4.20%
201214.40%16.00%32.00%
201318.20%32.40%64.80%
mean9.89%5.56%11.11%
Stdev0.0910.1990.398
compound rate9.51%3.60%1.64%
Investment of $100K on 1/1/2000$356,880$164,135$125,560

Buffet这些年的表现已大不如他的鼎盛时期,但仍然非常出色。先看看2xSPX(这只是模拟2x yearly performance,真的2x daily performance 更夸张)。这14年来有6年涨幅超过30%,只有2年跌幅幅超过30%,算术均值为11.11%,远高于BRK的9.89%。但BRK 14年的compound rate是9.51%,总收益是+256.88%,而2xSPX的compound rate只有1.64%,总收益只有+25.56%,连买bond都不如。为什么?答案在standard deviation 上,14年来BRK没有一次跌幅超过10%,也仅有一次涨幅超过20%,最高涨幅是区区21%(相信诸位牛人能轻松beat Buffet)。BRK standard deviation是0.091,而2xSPX有3次跌幅超过20%, standard deviation是BRK的4倍!看来问题出在下跌上,2008年下跌74%,那么上涨多少才能break even,记住:不是+74%,而是+285%!即以每年9%的速度,要连续增长15年才能break even!所以请记住Buffet的名言:Rule No.1: Never lose money. Rule No.2: Never forget rule No.1.投资规则第一条:不要亏钱,第二条:记住第一条!

所以在没有外来资金注入的情况下,如果被外婆,将take almost forever to recover。那么哪些证券能在时间无限的前提下,能实现不lose money呢 (beat inflation 另议)?只要能保证钱能生钱,生出来的钱总有超过principle的那一天!有interest或dividend的类别yield和风险从低到高大概有 CD,treasury bills, notes and bonds, municipal bonds, cooperate bond,real estate investment trust (REIT), utility stocks, preferred stocks, master limited partnership (MLP)。我们将在第三部分证券选择中讨论各种投资的利弊。

2. 复利的频率

一个被忽视的因素是复利的频率。股票或基金能每年发放一次红利,或每半年发放一次红利,或每季度年发放一次红利,或每月发放一次红利,如果每次都将红利reinvest,那么下次发放红利是就要根据最新的投资总额来派发,这就是复利增长。

我们仅比较一下APR (Annual Percentage Rate)是 4%,6%,和8%的情况下,monthly,quarterly,和annually compound的差别。

compound frequency
Annually
Quarterly
Monthly
Annually
Quarterly
Monthly
Annually
Quarterly
Monthly
yr4.00%4.00%4.00%6.00%6.00%6.00%8.00%8.00%8.00%
1$100,040$104,060$106,136$100,060$1,061,364$1,061,678$108,000$108,243$108,300
2$108,160$108,286$112,649$112,360$1,126,493$1,127,160$116,640$117,166$117,289
3$112,486$112,683$112,727$119,102$1,195,618$1,196,681$125,971$126,824$127,024
6$126,532$126,973$127,074$141,852$1,429,503$1,432,044$158,687$160,844$161,350
8$136,857$137,494$137,640$159,385$1,610,324$1,614,143$185,093$188,454$189,246
12$160,103$161,223$161,478$201,220$2,043,478$2,050,751$251,817$258,707$260,339
24$256,330$259,927$260,753$404,893$4,175,804$4,205,579$634,118$669,293$677,764
32$350,806$357,385$358,899$645,339$6,724,398$6,788,405$1,173,708$1,261,310$1,282,639

从中可以看到,如果是8%的APR,经过32年,monthly compound已经要比yearly compound的收入高出10%以上了。显然,在APR一定的情况下,发放红利的频率越高,最终的收益越高。如果这只股票能每月甚至每个星期都发红利,那就最好不过了。如果没有,我们可以创造条件,利用covered call或diagonal spread给自己发红利!

我们下次接着讨论。