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。

 

 

 

 

 

 

 

 

Chess and Trade (2)

If both chess and trade are games, why we keep playing these games?

Obviously, playing in this level of chess tournament cannot be justified by the financial reward. Even the champion, an National Master, spend 2 days played 6 games to won the cash award of $1800. There was not much left if taking lodging and transportation cost into account. Retail investors spend a great deal of time conducting market research and monitoring their portfolio. Even they might make decent profit, but after deducting commissions to brokers and tax to Uncle Sam, the yield will shrink substantially.

It is believed that to achieve genius level ability takes about 10,000 hours of practice or 10 years. Grand masters take about ten years of training and practice, only Bobby Fischer did it faster in nine years. It is a disappointing fact that most of us won’t be able to become a master or a professional trader, no matter how hard we try. That seems to be a typical high cost, long term, but low probability investment, which should be avoided outright.

We mentioned in the previous post, Louis Dembitz Brandeis, an associate justice of the U.S. Supreme Court, predicted a gloomy prospect for retail investors. However, Warren Buffet said:

“To invest successfully over a lifetime does not require a stratospheric IQ, unusual business insights or inside information. What’s needed is a sound intellectual framework for making decisions and the ability to keep emotions from corroding that framework.”

Here Warren Buffet’s emphasis is on the importance of high EQ (Emotional Intelligence). On personality development, chess games and investments offer excellent opportunities to improve observation skills, analytic skills, execution skills and ability and summarization skills. A high level chess players with high EQ is also very easy to excel in other areas. The founder of Grandmaster Capital Management, Patrick Wolff, is a grand master who won two US championships. He obtained Bachelor of Arts from Harvard University in Philosophy degree.

Let compare EQ requirements for a trade and a chess game:

(1) observation skills:
a chess: eg: That is straight forward. Which file is open? Which pieces are on the same line, a file, a rank or a diagonal?
b Investment: Does an event will influence our investment decision making? Such as: In Valley Fair Mall, Apple Store and the Microsoft Store are just across the corridor, we can clearly observe difference in traffic.

(2) analytic skills:
a chess: such as: How is the situation? Am I ahead or behind? Is my king safe? Are my other pieces safe? What is the most advantageous order if I have multiple ways of attack?
b Investment: eg: Is that event just a coincidence or becomes a confirmed trend? What was the market reaction? If I can take advantage of this opportunity, which stock I should choose as the vehicle? Are both fundamental and technical indicators cooperative? How long is the time frame?

(3) Execution skills:
a chess: Choose the safest way when you are advantageous. Be patient when you are behind. Always consider sacrifice, sometime even major pieces, to smash opponent’s defense.
b Investment: Take disciplined actions decisively, cut lose when necessary, do not dream a miracle will happen.

(4) Summerization skills:
Each trade should be recorded in the trade journal, analyze and review regularily. Avoid “step on the same rake twice”. Remember Dalai’s wisdom “When you lose, do not lose the lesson”!

Not everyone is suitable for trading, trading is a life long training of your mindset. Just treat every trade as an opportunity to exercise, so that we won’t make the same mistakes when managing more money in the future.

博弈与炒股[2]

如果炒股和下棋都是游戏,那么为什么我们乐此不彼?

下棋不能完全用物质来衡量。比赛的冠军,一位国际大师,花费2天时间获得奖金1800元,去掉交通住宿费用,事实上所得无几。散户花费大量时间研究股市,即使能够盈利,去掉commission和tax,真正到手的也不多了。一般认为,在任何一个行业成为大师级的人物,都必须花上10,000个小时,大约10年时间。不幸的是,即使花费了巨大的时间和精力,也只有极少数能成为投资高手或是象棋大师。典型一个high cost, long time frame, and low probability的案例,从投资的角度应该避免。

前文谈到美国最高法院大法官路易士·布兰戴斯(Louis Dembitz Brandeis)对散户投资者的前途严重不看好,而Warren Buffet却说 “要成功投资过一生不需要超高的智商,非凡的商业洞察力或内部信息。我们只需要有良好的知识框架来帮助我们正确的决策,和坚定的信念以防止这个框架免受情绪的侵蚀”。

“To invest successfully over a lifetime does not require a stratospheric IQ, unusual business insights or inside information. What’s needed is a sound intellectual framework for making decisions and the ability to keep emotions from corroding that framework.”

Warren Buffet在这里强调的是高EQ对投资重要性。在人格成长上,博弈与炒股都提供了绝佳的反复锤炼观察能力,分析能力,行动能力和归纳总结能力的机会。一个高水平的棋手在别的方面也很容易出类拔萃。Grandmaster Capital Management的创始人Patrick Wolff是一位曾两获美国冠军的国际象棋特级大师,从Harvard University获得Bachelor of Arts in Philosophy学位后却进入了资产管理行业。

微观比较一下一个trade和一盘chess game:

(1)观察能力:
a.国际象棋:如:哪些file open?哪些棋子在一条file,rank或diagonal上?
b.投资:身边或媒体上有没有发生影响投资的事件?如:在硅谷Valley Fair Mall里,Apple Store和Microsoft Store仅隔一条走廊,可以清楚的观察到客流的不同。

(2)分析能力:
a.国际象棋:如:大形势如何?我子力领先还是落后?我的王完全吗?我的其他棋子安全吗?我能用后,象,马三个不同的子check, 那么对我最有利的次序是什么?
b.投资:如:这个事件是偶然还是已经确认成一种趋势?以往发生这种情况市场如何反应?该选择那个股票来投资?FA和TA指标如何? time frame? expected return?

(3)行动能力:
a.国际象棋:优势时选择稳妥的致胜之道,劣势则相机而动,必要时弃子争胜。
b.投资:当机立断,顺市时了结或rollup,不顺时按计划果断平仓止损,不要幻想奇迹发生。

(4)归纳总结能力:
每个trade都要用trade journal记录下来,分析原因,定期回顾。避免“step on the same rake twice”。记住When you lose, do not lose the lesson!

并不是每个人都适合炒股,炒股就是a life long training of your mindset。把现在每个trade当成一次锻炼的机会,这样将来管理更多资金时不至于出现同样的错误。这下我们就不需要别的理由了!

Chess and Trade (1)

A few weeks ago, I took my son to People’s Tournament held at Santa Clara Convention Center in the heart of Silicon Valley. There were about 190 chess players from California and neighboring states, including 13 National Masters (NM), International Masters (IM) and Grand Masters (GM). Not too far away, Levis Stadium, the home of San Francisco 49ers will be open in a few weeks. I suddenly realized there are too many analogies between games and investments. New York Stock Exchange (NYSE), NASDAQ, American Stock Exchange (AMEX) are the playground like Santa Clara Convention Center and Levis Stadium, brokerage firms like Fidelity, eTrade, Interactive Brokers are organizers of the games, like National Football League and organizer of People’s tournament, they packet a profit no matter who wins the game. Institutions and Market Makers are masters or professionals who have an edge, sometimes dominantly, over retail investors, amateurs and neophyte players.

Trading stock is similar to playing games. Traders should take serious consideration of the following factors when opening a position:

  (1) Players: Stock market and chess are zero-sum games with winners and losers. The sum of winners’ gain of utility is about the sames as the losses of the losers, the other participants. A seemingly negligible portion is taken as commission or registration fee. The player should understand who is your opponent to choose the right strategy.

(2) Payoffs:For each opened position, we need to understand Max Return, Max Loss and Probability of all situations, such as break-even and exit. For the chess tournament, all registration fees ($100 apiece) will be pooled as award for winners. The champion of the open section will grab a cash reward of $1800, a ROI of 1,800%. However, it is very very unlikely an armature player to prevail in that section: although he may win a game by pure luck, the chance of winning a row of masters is simply too low! That is exactly the same as hoping a windfall in stock market.

  (3)Strategies:In a chess game, we can have Sicilian Defense, or Ruy Lopez /Spanish Defense and etc as openings. In stock market, We can open covered calls or naked puts, or more complicated as butterfly spreads and iron condors.

  (4) Orders:After opening, we will adjust our strategies based on the opponent’s response. We can use Marshall Attack, Karpov Variation and etc in Spanish defense. In option trade, we can utilize spreads to rollover our positions.

A game plan is required to ensure a high probability of success.

If both trading and chess are sorts of games, then Efficient market theory seems won’t be able to applied to stock trade. Efficient market theory can be summarized as followings:

  (1)Every player in the market is rational. They are closely monitoring all assets in the financial market, conduct fundamental analysis, evaluate the share price of each company and allocate asset accordingly prudently.

  (2) The share price reflect the balance of supply and demand. That is, the number of players who think the shares is overpriced is approximately the same as the number of players who think it is under-priced.

  (3) Stock price can fully reflect all available information of the assets, that is, “informationally efficient”, when changes in the information, the stock price will surely follow changes. When a good news or bad news just came out, the stock price began fluctuate, when it has become obvious, the price of the stock has gone up or down to the right price.

“Efficient market theory” actually means everyone in the rational case, no one can beat the market in the long run. However, (1), (2), (3) does not seem to be true, especially in the player’s level. Masters (USCF National Masters need to achieve a rating of 2200) and Market Maker generally have after a long hard training, proficient at dealing with complex situations, rarely make a blunder. Most financial products do not have enough liquidity, and prices tend to be manipulated. Secondly, if you have the opportunity to compete for the World Masters champion, behind the coaching team will help master data collected opponent, a comprehensive analysis of the merits of their opponents, to develop corresponding strategies. Investment banking institutions tend to have a large team of analysts, focused analysis of each sector, a variety of asset, governments trends, including members of Congress to inquire into the attitude of the bill. Most retail investors won’t have the resource to match the professional players and are likely to be slaughtered in unfair games.

Louis Dembitz Brandeis, an associate justice of the U.S. Supreme Court once wrote:

“For a small investor to make an intelligent selection from these many corporate securities — indeed, to pass an intelligent judgment upon a single one — is ordinarily impossible. He lacks the ability, the facilities, the training and the time essential to a proper investigation.”

I am not saying there is no chance for an amateur to win a master. A master may make a blunder occasionally, but it is more likely he can survive and thrive after setbacks. Unlike stock market, game organizers like to divide players in different sections based on their levels/rankings. There are some asset categories. often associated with low liquidity and high risk, such as options and junk stocks, lack institution investors, but are Eden of retail investors. Please do not forget when you make huge profit, there is another retail investor might just lost his pants. The next one who lost his pant may be you and me.

The question now becomes whether it is necessary to spend myriad of time and energy to become a master. Or whether I can become a master even I spend myriad of time and energy.

博弈与炒股[1]

几周前我带小朋友参加加利福尼亚州的大众棋赛(People’s Tournament)。比赛在硅谷的中心Santa Clara Convention Center举行,来参赛的有附近几个州的190名棋手,其中有13名带帽子的,大师 (National Master NM),国际大师 (International Master, IM)和国际特级大师 (Grand Master GM)。看着不远处即将投入使用的旧金山49人队的主场Levis Stadium,突然想到炒股和体育比赛和下棋有许多相似之处。NYSE/NASDAQ/AMEX 相当于Santa Clara Convention Center和Levis Stadium, Fidelity/eTrade/Interactive Brokers相当于National Football League和People’s Tournament的组织者,机构大户Market Makers相当于这些带帽的master们,散户-散户是和我们家小朋友这样的青蛙们。

其实炒股和其他体育比赛一样,玩家在open position时必须仔细考量到博弈的几个要素:

  (1)局中人(players):股市和棋赛都是“多人博弈”的零和游戏,有赢家和输家,且输赢的数目相当,多的被exchange和broker抽走了。玩家需要清楚的明白对手是谁,才能制定正确的对策。

(2)得失(payoffs):炒股是需要明白Max Return, Max Loss和各种情况的probability,棋赛-本次比赛报名费$100,但MMs 免费入场!棋赛的reward跟参赛人数有关,本次比赛公开组冠军奖金$1800, 如果拿到第一,ROI是18倍!可是,一个未经过专业训练的棋手拿到最高奖的可能性就太低太低了!

  (3)策略(strategies):棋赛可以西班牙开局,也可以以西西里防御开局。炒股可以有covered call, naked put,也可以有玩花的butterfly spread和iron condor。

  (4)次序(orders):开局了,还要根据对手的变化,适时调整,如果以西班牙开局,还可以有马歇尔攻击奇戈林变例。玩option也可以根据形势用spread来rollover。

如果炒股和下棋一样是一种博弈,那么有效市场理论(Efficient market theory)就是无法实现的。“有效市场理论”包含以下几个要点:

  (1)在市场上的每个人都是理性的经济人,金融市场上每只股票所代表的各家公司都处于这些理性人的严格监视之下,他们每天都在进行基本分析,以公司未来的获利性来评价公司的股票价格,把未来价值折算成今天的现值,并谨慎地在风险与收益之间进行权衡取舍。

  (2) 股票的价格反映了这些理性人的供求的平衡,想买的人正好等于想卖的人,即,认为股价被高估的人与认为股价被低估的人正好相等,假如有人发现这两者不等,即存在套利的可能性的话,他们立即会用买进或卖出股票的办法使股价迅速变动到能够使二者相等为止。

  (3) 股票的价格也能充分反映该资产的所有可获得的信息,即”信息有效”,当信息变动时,股票的价格就一定会随之变动。一个利好消息或利空消息刚刚传出时,股票的价格就开始异动,当它已经路人皆知时,股票的价格也已经涨或跌到适当的价位了。

  ”有效市场理论”实际上意味着在每个人都很理性的情况下,任何人都无法长期beat the market. 但是, (1), (2),(3)似乎都不成立,尤其反应在玩家的水平上。
大师(美国 USCF National Master 需要达到等级分2200)和Market Maker一般都得经过长期艰苦的训练,善于应对盘中各种复杂的形势,绝少犯低级错误。大多数金融产品的流动性不强,价格往往被操纵。其次如果大师能有机会角逐世界冠军,背后的教练团队会帮助大师收集对手的资料,全面分析自己和对手优劣,制定相对应的策略。投行机构往往有庞大的分团队,专注分析各个sector,各种asset,各国政府动向,包括打探国会议员对各项法案的态度。不难想象大多数散户投资者成为机构slaughter的对象。

美国最高法院大法官路易士·布兰戴斯(Louis Dembitz Brandeis) 曾说:
对于中小投资者,以做出明智的选择,从众多股票中做出一个明智的判断 – 通常是不可能的。他没有能力,设施,训练,和充分的时间做适当的调查。

“For a small investor to make an intelligent selection from these many corporate securities — indeed, to pass an intelligent judgment upon a single one — is ordinarily impossible. He lacks the ability, the facilities, the training and the time essential to a proper investigation.”

与专业玩家博弈,不是没有机会,但笑到最后的很可能是这些MM们。体育比赛为确保观赏性,会把相同档次的玩家放在同一个section里 (玩家也可以交钱play up尝尝被虐的滋味)。这样在没有专业玩家的赛场上,每个都有公平的机会。一些流通性较低,风险较大的市场,如期权,垃圾股和问题股正式散户翻云覆雨的舞台。但请不要忘记当你make huge profit时,就有另一个散户被看到脚踝上。而下一次(或下某次)被砍到脚踝的可能就是你和我。

我们有必要花费巨大的时间和精力成为master吗?或是,即使我们花费巨大的时间和精力,我们能成为master吗?

Two Mid Term Near The Money Call Trade Lessons:TSLA & SYNA

We discussed utilize near the money (NTM) calls to ride the momentum of an ascending stock in the previous article.  Stocks which meet the ‘3M’ criteria might have better chances to outperform the market.

1)Momentum: The underlying stock just breaks up and is in a confirmed uptrend, which is supported by favorable technical indicators and fundamentals.

2) Multiple non-correlated evidences, such as:

  •  The stock is recommended by Investors Business Daily and/or  Barron’s, such as it is on IBD Top 50 or one of the sector leaders.
  •  Phenomenon observed by myself, such as long line when dinning at Chipotle Mexican Grill, more electric cars on streets or in parking lots, more handbags of a brand, a full house of customers in Nordstrom, huge new job listing of your neighboring company (which usually means a M&A event might be imminent)
  •  Outperforming sectors:such as new energy, biotech and internet stocks of last year.

3)Market: We expect market will remain stable or maintain the uptrend. However, if there is a significant correction, most stock will go down with the broad market, no matter how pretty your chart appears to be.

I would like to use my own recent trade experience to help others get a better understanding of Near-The-Money calls.

 TESLA (TSLA)

The Parking Lot of Computer History Museum, Mount View, California

The Parking Lot of Computer History Museum, Mount View, California

My initial position was established in 2009 with an average cost of $22. At that time, I just relocated to Silicon Valley and spend most of my effort working on a startup I co-founded with my friends while keeping an eye on emerging opportunities. Without a mature methodology, I purchased some Tesla shares just because that 100% electric car seemed to be a cool idea for me. Tesla share price had been fluctuated up and down from 2009 to 2013 and Tesla (the car) and TSLA (the stock) had not gained a spot in the Hall of Fame yet. I did not pay much attention until 2013 when I overheard Elon Musk talking about his great venture of Tesla and SpaceX on NPR (National Public Radio) [1]. In the early Spring of 2013, I spotted more and more Tesla cars when I was walking to the park, when I was on traffic duty and when I was in a parking lot [2]. The following  picture was taken on in the parking lot of The Computer History Museum, Mount View, California. My friends in other states confirmed they observed the same phenomenon [3]. Indeed, Tesla is becoming a fashion among the riches [4]. Meanwhile, it has been confirmed Tesla bumped up its productivity by tracking VINs, but still could not match the escalating demand [5].

TSLA started its brilliant run at early 2013. It appreciated 40% and touched $55 in early May. Elon Musk joked about a historical break even quarter. So far Tesla met all requirements of the 3Ms; a confirmed uptrend, a favorable fundamentals, multiple non correlated evidences (endorsements from reputable media, VINs and increasing popularity) and a stable stock market. Since Tesla was going to release the earning report on May 10, 2013, TSLA stock became more volatile. High vega ballooned the call price. A call option which strike is $15 (23%) out of the money and expire 4 months later was asked for $3.30. It might be hard to tell whether the SEP 21 13 $70 Call was still near the money, but I still want sufficient time to ride the uptrend. Fortunately, the rest of the story  unfolded as expected and  TSLA had a tremendous run! Tesla stock gapped up after earning report on May 10, 2013. The robust uptrend easily lasted more than 2 month. I closed all positions with 500% reward. At TSLA SEP 21 13 $70 Call expiration day, share price is 181, a.k.a this call had an intrinsic value of $111, which is 33,600% higher. Someone must have an extremely strong nerve to hold it!

I felt pure lucky for this kind of play. The chance of picking a super bull from thousands of stock are thin. I believe luck is balanced somehow. You won’t be able to lucky for a long run! I mentioned that the first 2Ms,(momentum and multiple irrelevant evidences) are not sufficient to make a trade successful ,if market tanks,the Near The Money Call strategy is hard to be profitable although there might be thousands of evidences.

Sep 21 $70 Call Purchased on May 7th, 2 days before earning report.  TSLA reached $181 at the expiration day

Sep 21 $70 Call Purchased on May 7th, 2 days before earning report. TSLA reached $181 at the expiration day

SYNAPTICS is such a painful lesson I learned. SNAP was in confirmed uptrend since the beginning of the year of 2014. Synapitics is frequently featured on Investors Business Daily’s Top 50 and Sector Leaders. Both Technical Analysis and Fundamental Analysis suggested that the company are in good track to bump up its profit. Some friends of mine left their admirable positions and joined Synaptics, which means SYNA was expanding rapidly. It seemed to be a perfect setup since SYNA easily met all requirements. I purchased $SYNA 19 APR14 65.0 C call which is at the money (ATM) call and have 2 months to run. However, there was a market correction lasted 2 months, SYNA never touched the strike price again in the next 2 months! All of my SYNA calls expired worthlessly! I immediately deleted SYNA from my watch list. However, a few month later, SYNA touched a new high of $92! Actually, it wad in the money right after the cell expired!

SYNA was below $65 until my $65 calls expired. It then advanced to $90

SYNA was below $65 until my $65 calls expired. It then advanced to $90

The take message: It is much difficult to profit from call purchase since we should take strike price, expiration date and the momentum of the underlying stock. Time erosion is still a haunting threat to the call owner.  Sometimes you get tailwind, sometimes the wind turns against you.

Next time, I will introduce Deep In The Money Call to replace margin.

 

中期Near The Money Call 实例:TSLA和SYNA

前文讨论了利用Near The Money Call在股票维持上涨动能时盈利, 提到了自创的3M理论来pick,即 Momentum, Multiple non-correlated evidences 和 Market。

1)Momentum(动能): 股票正处于突破后的上升趋势中, 有良好的TA指标和基本面。

2) Multiple non-correlated evidences (多个互不关联的证据),如:

  • 大牛, Investors Business Daily 或 Barron’s 推荐, 如 stock on IBD Top 50 or section leader
  • 客观观察到的经济现象: 如CMG要排长队,LD最近爱到Nordstrom 扫货,街上和parking lot里某种牌子的电动车大增,隔壁某公司忽然大举扩张(通常是并购前兆)等。
  •  Outperforming sectors: 如去年的新能源,生物科技和互联网等

3)Market(大市走向):我们期望市场平稳或上扬,但如果出现较大幅度的调整, 股票往往会跟随大市向下, 再好的momentum可能也无济于事。

以下是我个人经历,希望能帮助大家加深对期权的理解有所帮助。

TESLA (TSLA)-特斯拉

刚开始留意TSLA时是$22左右(后面没有0), 记得微博上关注的朋友吼了一嗓子,当时刚到硅谷,正在热血沸腾创业中,觉得电动车这个概念有点意思,就入了点,放在那里忙startup去了,结果一放就是N年,期间上上下下,都没有太在意。到了2013年,开车听收音机NPR刚好在谈Elon Musk的宏伟计划【1】,以前TESLA是稀罕之物,但此时硅谷的TESLA电动车越来越多,几乎每天都能看到好几辆【2】。这是我2013年某日在位于山景城的Computer History Museum的Parking Lot里拍摄到的。和别州的朋友,他说也观察到了同样的现象【3】。碰巧在微博中有位土豪朋友说他准备入一辆特斯拉电动车,感觉Tesla正在成为一种fashion【4】。我想车买不起,好歹买些Option,没准还能赚到一辆车呢!

The Parking Lot of Computer History Museum, Mount View, California

The Parking Lot of Computer History Museum, Mount View, California

当时买到车的人都把VIN 贴出来,可以看出Tesla产能大增,但仍供不应求【5】。

Tesla到2013年初即开始上涨,当时还没这么出名,到5月初上涨了40%到$55,当时Elon已经放出风来,Tesla会第一次实现break even。TSLA已基本满足了‘3M’的条件。知名媒体造势,TA, FA都不错,5个不相关的证据表明公司正在高速发展,整个股市也没有大的起伏。因为将在2013年5月10日公布财务报告。因为振幅巨大,二个月后到期的Option被炒得很高,但还是一咬牙以$3.30入了SEP 21 13 $70 Call,已经基本不算是Near The Money Call了,但我还是希望有更多的时间ride the uptrend。结果如我所愿,TSLA在5月10日ER后大涨,并在接下来的2个月内一直保持强大上涨动能,轻松翻倍。我在实现>5倍利润后了,逐步减仓出场。当时对call followup action还没有使用娴熟,否则roll up或roll forward都可获利更多。该合约到期时TSLA的股价为$181,即call的intrinsic value是$111,已上涨了33.6倍!可是谁又能hold住?

Sep 21 $70 Call Purchased on May 7th, 2 days before earning report.  TSLA reached $181 at the expiration day

Sep 21 $70 Call Purchased on May 7th, 2 days before earning report. TSLA reached $181 at the expiration day

仔细想来,在数千只股票中挑出大牛股纯属幸运。而命运是公平滴,你总得匀别人一点。我在前文也提到前面的2个M(momentum和multiple irrelevant evidences)只是必要条件,如果没有Market配合,有一千个靠(call)它的理由,如果市场在从购买期权到期权到期这段时间如果出现较大的调整,还是很难获利。

SYNAPTICS就是这么个惨痛滴血本乌龟的经历。今年开始SYNA一直不错,它家的股票也是IBD Top 50 和Sector Leaders 的常客,TA (Technical Analysis), FA (Fundamental Analysis)要多棒有多棒。更为严重的是,身边有几位曾在硅谷知名公司工作过的朋友跳槽到了Snaptics,表明该公司进入了新一轮高速发展期。(在上市公司密集的地方,只要注意观察,不需要提前看到财务报表,也可能发掘到很多机会,以后在专文讨论)Snaptics的确就是个机会,它轻松满足所有的条件,我“果断”以$4.30入了2个月到期的SYNA 19 APR14 65.0 C call(当日的股价为$65),。人算不如天算,在我入场后,大势开始了一轮长达2个月的调整, SYNA一直在strike price 之下,看着theta (time decay)一点 一点的蚕食,心里一直在纠结是否要追加投资roll forward。最后决定不追,由它去吧!到了expiration day, SNAP还是没到$65, 靠, 一文不值了! 我恶狠狠滴把SYNA的sticker从我的watch list 上删掉了!

SYNA was below $65 until my $65 calls expired. It then advanced to $90

SYNA was below $65 until my $65 calls expired. It then advanced to $90

谁知几个月之后,我无意中又看了SYNA一眼,发现在call到期的第二天就一跃in the money,而且几个月连续上涨到$90多!一天之差,我见了外婆!

总结:期权要考虑到股票,strike & expiration date,当然比纯买股票难很多!所以赌动能也不靠谱, time erosion 太可怕了!所以不中是应该的,中了是运气。懂Monte Carlo的童鞋请帮忙算算长期回报。

下回介绍用Deep In The Money Call取代margin的办法。

Mid Term Call Strategy – Near The Money Call

We briefly discussed the short term strategy which utilizes DOTM (Deep Out Of The Money) Call to bet earning report. The stock can go either direction to certain level. Nevertheless, there is a option strategy to make a profit: We might long calls to profit from sudden jump, long puts to profit from plummeting stocks, long strangles or straddles, short iron condors to profit from drastic movement in either direction, or you might bet against no drastic, but no movement or mild movement by longing iron condors or shorting strangles/straddle. However, you should remember no matter what kind of setup you decide to take, your counterpart, very likely a market maker (MM), has already place the bid based on their sophisticated algorithm which is in favor of themselves. At the end of day. I mean at the end of market close of expiration day, MMs are likely the ones who profit eventually.

In the previous discuss of short term strategy,  theta (time decay) is the archenemy of DOTM (deep out of the money) near expiration call owner and the stock must appreciate rapidly. Theta can be found to describe the negative impact of time (i.e decreasing time value) pass to option price for both calls and puts. If delta is -0.80 (delta is always negative unless we can rollback the clock), which means the option will be devalued by $0.80 if other factors remain the same. The diminishing of time value accelerates when there is only 2 weeks left and race to the climax on the expiration day. If you need more leeway to allow your stock of interest to appreciate, you can choose Near the Money (NTM) Call which has approximately 2 months to expire. By that way, we will have sufficient time to ride the tide, but also have followup strategies when the tide is against us.

Each person has his own standard to pick stocks. I personally prefer the self-invented “3M” system to increase the probability of success:

1)Momentum: The underlying stock just breaks up and is in a confirmed uptrend, which is supported by favorable technical indicators and fundamentals.

2) Multiple non-correlated evidences, such as:

  •  The stock is recommended by Investors Business Daily and/or  Barron’s, such as it is on IBD Top 50 or one of the sector leaders.
  •  Phenomenon observed by myself, such as long line when dinning at Chipotle Mexican Grill, more electric cars on streets or in parking lots, more handbags of a brand, a full house of customers in Nordstrom, huge new job listing of your neighboring company (which usually means a M&A event might be imminent)
  •  Outperforming sectors:such as new energy, biotech and internet stocks of last year.

3)Market: We expect market will remain stable or maintain the uptrend. However, if there is a significant correction, most stock will go down with the broad market, no matter how pretty your chart appears to be.

We can purchase a high value, liquidated stock with delta around 0.5 and expect a ROI of 3-5 folds.

Here is a breakdown analysis of Greeks and I just assign an subjective probability value for simplicity:

delta: Let’s just assume we have a very nice pick and the uptrend will maintained. The probability of a winning delta is 80%.

gamma: The movement  (of either direction) can be accelerated or decelerated, P = 50%.

vega: If only consider the price of the expiration day, vega is not relevant.

theta: The time decay of the 1st one and half months are still manageable. Let’s just assume it will devalue 30%, or 70% favorable.

Overall, we have probability of 28%, not bad if we can gain 5x ROI.

Take home messages:

1. relatively low probability (not terribly low as DOTM),relative high ROI (not as high as DOTM),limited loss.

2. Followup possible: If the stock appreciates but time is running out, we can roll forward. If the stock is skyrocketing, we can roll up and let the profit run.

3. replicable, but ROI is not guaranteed. If we are successful one out of three trades (100% loss in 2 trades), we are only break even when we get 300% ROI on the winning trade. However, the probability of higher ROI will go much lower.

4. Not scalable: Except for those high volume liquidated stocks, Market Makers won’t allow you to purchase a great deal of NTM calls. They will lift the ask price when you are buying.

In essence, we can optimize our approaches to make right picks by refine our technical analysis and fundamental analysis, we can reveal more irrelevant events to predict the direction of the underlaying stock. However, we do not have the capacity to control the market and avoid adverse impact of an unexpected events. Thus, a prudent investor should have a sound exit strategy in mind before he press the buy button. Good luck!

 

买Call中期策略- Near The Money Call

上次讨论了短期策略利用DOTM (Deep Out Of The Money) Call来赌 ER。当然赌earning report的各种各样的期货玩法。赌剧烈运动的可以bet大涨 (long call),大跌 (long put), 大涨或大跌 (long strangle/straddle 或 short iron codor), 也可以bet小幅波动  (short strangle/straddle 或 long iron condor)。请牢记无论选择那种玩法,您的对手(买方/卖方),Market Makers一定计算好了的赔率并设定了对他有利的价格,笑到最后的很可能是他们。

在短期策略中, theta (time decay) 对call持有者是个巨大的威胁,股票必需在很短的时间内快速上扬。这里theta用来表示时间对期权价格的影响。如果theta指为-0.80 (注意theta 只能是负值),这表明在股价和其它因素不变的情况下,第二天该期权的价格将下降80c。通常对有time premium 的call在最后两个星期,time value开始显著下降,到expiration day达到最低值并趋向0。如果您需要更多时间让股票增值,可以选择二个月左右的Near the Money (NTM) Call, 这样就有充分的时间ride the momentum, 如果风向不对,也有机会补救。

个人有不同的选股标准,我比较倾向于我自创的3M体系来提高成功率:

1)Momentum(动能): 股票正处于突破后的上升趋势中, 有良好的TA指标和基本面。

2) Multiple non-correlated evidences (多个互不关联的证据),如:

  • 大牛, Investors Business Daily 或 Barron’s 推荐, 如 stock on IBD Top 50 or section leader
  • 客观观察到的经济现象: 如CMG要排长队,LD最近爱到Nordstrom 扫货,街上和parking lot里某种牌子的电动车大增,隔壁某公司忽然大举扩张(通常是并购前兆)等。
  •  Outperforming sectors: 如去年的新能源,生物科技和互联网等

3)Market(大市走向):我们期望市场平稳或上扬,但如果出现较大幅度的调整, 股票往往会跟随大市向下, 再好的momentum可能也无济于事。

我们可以选择流动性较高, 股票价格较高(以后专文讨论),delta 0.5左右的call,预期获得3-5倍的回报。

大概分析一下Greeks对期权价格的影响:

delta: 假定该股票会保持趋势,继续上行,胜率 80%。

gamma: 加速减速各半,各 50%。

vega: 振幅可高可低,但如果只考虑到期日的情况,则与之无关。

theta: 前1个半月theta的影响较小, 假定 70%。初步算来盈利的可能性为28%

总结:

1. 较低概率,较高回报,损失有限, 但盈利无上限。

2. 可以有后续手段: 如果上涨但速度不够, 您可以Roll forward得到跟多的时间,如果快速上行,您可以roll up 获得更高的利润。

3. 可重复,但收益难以保证:假如买对3次,一次成功(33%)得到3倍的回报,其他2次亏光,ROI仍是0。如果成功的那次得到5倍的回报,则ROI为67%。

4. 不可规模化:除某些交易量巨大的股票外(如GOOGL),您也不可能以同样的低价格购买到大量的 NTM call。在您买进的同时,MM会逐步抬高call的价格。

总之,我们可以优化我们利用技术指标来判断动能的方法,可以找到更多不互相关联的证据来支持股票上涨的观点。但我们无法左右大盘的走向和突发事件的发生,投资者应该在买入时就有exit  strategy,有备无患。下文将分享我个人的经验和教训。