Accounts and Earnings

#Account Net Value

The net value of the account refers to the final fund balance of an account if the assets currently held are closed. For example, suppose you have 1 million, and you bought 600,000 shares of Apple, and later these stocks rose to 800,000. At this time, your account net value is 400,000 cash + 800,000 stocks = 1.2 million.

#Annualized rate of return and cumulative rate of return

#Cumulative Rate Of Return
For example, if someone invests 100 yuan, it will be worth 150 yuan two years later, and the total income in these two years will be 50 yuan.
(150/100)-1= 50%, 50% is the cumulative rate of return, since it is 2 years, then divided by 2 to get 25%, which is the Average Annual Growth Rate.
It is equivalent to if you use a fixed principal every year, you will get a 25% return every year.

#Annualized Rate Of Return
The concept of annualized rate of return is relatively easy to understand. It is mainly used in the introduction of some financial products, such as wealth management products such as Yu’e Bao and currency funds. Generally, there will be a so-called “7-day annualized rate of return”, assuming it is 2%. In fact, it is assumed that the income of this wealth management product can maintain the level of the previous 7 days in the next year, then holding it for one year can get 2% of the overall income.

#Compound interest and compound annualized rate of return

#Compound Interest

Assuming that a person buys a product with a fixed rate of return of r with the initial principal, he can receive interest money every year. If the interest is involved in the investment every year, then obviously due to the increase in the investment principal in the next year, he will also receive interest money every year. To get more interest, then in the N year, the principal is actually two parts, the initial principal, and the accumulated interest earned in the previous N-1 years. If N is long enough, the latter can be much greater than The former, and this “rolling interest” method, once the time is long, will eventually produce a very amazing income, which is compound interest.

“Compound interest is the eighth wonder of the world, and its power even exceeds that of the atomic bomb.” This sentence is said to be said by Einstein. Let us figure out how powerful it is. The calculation formula of compound interest is actually very simple. Using the above example, the final value = initial principal * ((1+r) to the Nth power), here we might as well assume that the principal is 10,000 yuan, r is the annual rate of return, assuming It is 5%, and N is the duration. Assuming it lasts for 30 years, what is the final compound interest?
10000*(1.05 to the 30th power)=43219, which becomes more than 40,000.
What if the annual rate of return is 10%?
10000*(1.10 to the 30th power)=174494, which becomes more than 170,000.
What if the annual rate of return is 20%?
10000*(1.20 to the 30th power)=2373763, which becomes more than 2.3 million!
It can be seen that compound interest is greatly affected by annual income, so assuming that one year does not generate any income, so the 30 years with income become 29 years, then the final compound interest is:
10000*(1.20 to the 29th power)=1978136, which becomes less than 2 million! Less than 1 year is less than 300,000! It can be seen that the key to compound interest is stable profit and duration.

#Compound Annual Growth Rate
Going back to the example of the rate of return for years, a person invests 100 yuan, which is worth 150 yuan two years later. The total income in these two years is 50 yuan. The calculated rate of return for years is 25%. What about an average annual return of 25%? No, because in fact, he may earn 25 yuan after the first year, and earn another 25 yuan in the second year with a principal of 125. He used compound interest here, but obviously, he did not reach the average return of 25%. rate, if 25% is brought into the compound interest formula, the value calculated here is wrong: 100*(1.25**2)=156.25, and the correct value should be 150.

So how to calculate his real average annual rate of return? Quite simply, we know that the compound interest formula is
Final value = initial principal * (Nth power of (1+r))

so you can get
r= ((final value/initial principal) to the Nth power)-1

Using the numbers in the example to calculate ((150/100) square root -1 = 1.5 square root -1 = 22.5%, so his annual average earning power is 22.5%, which is also called compound annual rate of return, or GARG for short. This is also an important evaluation indicator for investment products and investment capabilities.

#Maximum Drawdown and Maximum Drawdown Time

Retracement refers to the decrease in the net value of the account during a certain period of time when the net value of the account falls from a very high value until the net value falls back to a very low value. A retracement generally specifies a minimum range, for example, a drop of more than 10% from the previous high is called a retracement. In the selected time period, sometimes there will be several retracements, the largest of which is called the maximum retracement. For example, suppose you bought the stock price of Facebook with full position, so the net value of your account is in line with the trend of Facebook stock price.

First of all, choose a time period. We assume that the calculation starts from point a and ends at point d. Then which period is the maximum retracement? The answer is from a to b, because:

The drop from c to d is obviously not as big as the drop from a to b
Point c is higher than point a, so can the section from c to b be calculated as the maximum retracement? No, the maximum retracement is not the selected highest point net value minus the lowest point net value. Its calculation must start after the low point net value occurs after the high point net value, because this is in line with the real maximum net value retracement.

The maximum retracement is actually also called the maximum retracement rate, because it represents a percentage. Let’s take Facebook as an example above. Point a assumes that the price is 220, and point b assumes that the price is 120. Then the maximum retracement is (1-120 /220)=45.5%, in other words, I bought 1 share of Facebook stock, the net value of the account was 220 at the highest point, and then fell to 120, the net value of the account fell by 45.5% from the highest point! This retracement is relatively large, especially for those who bought at the highest point. The largest retracement also indicates the biggest loss they face. For those with poor psychological quality, they may sell during the decline. It will not be able to persist until the subsequent rebound. Therefore, the maximum retracement rate is actually an important indicator for investors to examine investment products and investment capabilities.

The maximum retracement time is also relatively easy to understand, which is the period of maximum retracement (the period from a to b).

For example, if the 10-year compound annual return rate of a product is 30%, the return is of course amazing, but its maximum drawdown rate is 50%, in other words, there has been a 50% drop in net worth during the period, or The maximum retracement is 20%, but the maximum retracement time is 5 years, that is, although the retracement is small, it stops in a certain range for 5 years in the middle and does not break a new high. So as an investor, do you have the confidence to buy this investment product? Not every investor has the psychological quality to accept such a sharp drop. Some investors would rather choose products with lower investment yields but relatively stable net worth growth.

#Average Drawdown and Average Drawdown Time

After understanding the maximum retracement and the maximum retracement time, in fact, understanding the average retracement and the average retracement time is a matter of course. First, specify a minimum decline rate such as 10%. When the net value of the account falls by more than this ratio, it is considered a retracement. Then The magnitude and time of each retracement within a period of time can be counted, and the average value can be calculated at the end.

The average retracement and average retracement time are also indicators to see whether an investment strategy is stable or not.

#sharpe rate

The Sharpe ratio, also known as the return-to-volatility ratio, is probably the most commonly used metric for portfolio management. formula:
(expected rate of return – risk-free rate) / portfolio standard deviation

Suppose you create a portfolio, and you can get the annualized rate of return of the portfolio for each year through historical data, such as 10% in the first year, 15% in the second year, -8% in the third year, and -8% in the fourth year 12%. . . You can use this array to calculate the return standard deviation of this portfolio, assuming it is 6%.

The so-called risk-free interest rate is the interest rate you can get if you invest in an asset without any risk. Generally speaking, the United States is unlikely to go bankrupt, so the US 10-year Treasury bond rate is often used as a risk-free rate for model calculations.

Assume here that the risk-free interest rate is 3%, and the compound annualized rate of return of your investment portfolio is assumed to be 15%, then 12% can be obtained by using 15%-3%, which means that you exceed the risk-free interest rate, and then use 12 % divided by the standard deviation of the portfolio 6% = 2, which means that every 1% increase in the risk of the portfolio will result in an additional return of 2%. Obviously, the bigger the Sharpe ratio, the better.

#Average profit rate, average loss rate, profit-loss ratio

Suppose you complete 100 opening and closing positions in one year, 60 of which are profitable, and these 60 cumulative profits account for 60,000, 30 of which are losses, and these 30 cumulative losses account for 60,000, and there are 10 more No profit and no loss.

Then, your overall investment this year is 60,000-60,000=0. The specific details include:

Profit ratio: also called winning rate, profit times 60/transactions 100=60%.
Average profit: cumulative profit 60000/profit times 60=100, so you earn an average of 100 yuan for each profitable transaction.
Average loss: cumulative loss 60,000/number of losses 30=200, so you lose an average of 200 yuan in each losing transaction.
Profit-loss ratio: average profit 100/average loss 200=50%.

It can be seen from the above that although your winning rate is relatively high, greater than 50%, but because the average profit is less than the average loss, the profit and loss are relatively poor, so you did not make any money in the end.

In the same way, to examine whether an investment product (or investment strategy) and investment ability are stable, in addition to the maximum retracement, you can also examine the average retracement rate, average retracement duration, and maximum retracement time during this period.

The above indicators are all important indicators for examining investment products (or investment strategies) and investment capabilities.

Usually, when institutions do quantitative models, these indicators are also used to evaluate the model.

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