Summary: Investors put the principal C into the market, and its market value becomes V after time t, so this investment: 1, return =V-C 2, yield: K=P/C=(V-C)/C=V/C- 1 3, annualized yield: (/kloc) Y = ( 1+K) N-660。 D stands for the effective investment time of one year, with bank deposits, bills and bonds being D=360 days, stocks and futures being 250 days, and real estate and industry being D=365 days. 4. In the case of continuous multi-period investment, y = (1+k) n-1= (1+k) d/t-1,where: k = ∏ (ki+1. 2. The amount and speed of earning compensation are expressed by annualized rate of return. 3. The benchmark of investment success or failure is: 5-year bank time deposit interest rate, 10-30-year long-term treasury bond yield, inflation rate of the year, and market index yield of the year. Only if the annualized rate of return exceeds the highest of these four standards can the investment be considered successful! How to calculate the annualized rate of return? Let's look at a simple example first: one-time investment. Suppose an investor invests the principal C in a market (such as the stock market) at a certain moment, and its market value becomes V after a period of time t, then the investor's income (or loss) during this period, if V is here, the effective investment time d of one year varies with the market. Such as bank deposits, bills, bonds, etc. Interest is generally calculated at 360 days per year (or 365 days in rare cases), that is, D=360 days. In publicly traded markets such as stocks and futures, the effective investment time is the number of trading days in a year, which is about 250 days after deducting holidays (52 weeks a year, 5 trading days a week, about 10 holidays a year: 52×5- 10=250), that is, D=250 days. Used in real estate, general commerce, industry, etc. Because you can buy, sell or open positions every day, it is not affected by holidays, so the effective investment time is the natural days of the year, that is, D=365 days. Very special circumstances, such as an extra day in individual years caused by leap years, can naturally be ignored because of their small impact. For example, suppose investor A invests 1 0,000 yuan (C = 1 0,000 yuan), and after one month, the market value will increase to 1 654,38+0,000 yuan (V = 1 654,38+) Then the return on this investment is K=P/C= 10%. Because there are 12 months in a year, the same investment can be repeated 12 times a year (N=D/T= 12), so its annualized rate of return is y = (1+). In other words, earning 10% a month is equivalent to earning 2. 1384 times a year. If investor A repeats this investment, the principal of 1000 yuan can be increased to 3 1384 yuan after one year. On the other hand, if the investor unfortunately loses 1 000 yuan per month, then the net income of this investment is P =-0. 1 000 yuan, the yield is K = P/C =- 10%, and the annualized rate of return is y = (1+). That is to say, if the investor loses 10% every month, he will lose 7 1.76% of the principal one year later, and by the end of the year, his 10000 yuan principal will only be 2824 yuan. What about earning 10% a day? For example, the stock bought at yesterday's closing price is lucky to earn a daily limit today, so how high is its annualized rate of return? Obviously, the rate of return here is K= 10%, and the number of days that can be reinvested in a year is the number of trading days in a year, that is, N=250. So the annualized rate of return is y = (1+k) n-1=1.250-1≈ 2.2293×10, kloc-0/0. In other words, if investors earn a daily limit, the initial principal of 1 000 yuan will increase to 222.93 trillion yuan after one year! How rich you are! ! On the other hand, if the investor unfortunately encounters the daily limit, the yield is K=- 10%, and the annualized yield is y = (1+k) 250-1= 0.9250-1≈ 3.636×1. Obviously, the investor's principal is all lost! Let's look at the second example. Investor B made a long-term profit of 3.6 times in 28 months, that is, the initial investment principal was 1 000 yuan, and it increased to 46,000 yuan after two years and four months. The investment time of this investment here is T=28 months, so the number of times it can be repeated every year is N=D/T= 12/28. The return rate of this investment is K=360%, and the annualized return rate is y = (1+k) n-1= 4.612/28-1≈ 92.33%, which nearly doubles every year. If investor B's second long-term investment is a loss of 68% in 35 months, that is, the initial investment is 6,543,800 yuan, and the principal is only 3,200 yuan after two years of 654.38+065.438+0 months. Then the investment time is T=35 months, N=D/T= 12/35, and the yield is -68%, so the annualized rate of return is y = (1+k) n-1= 0.3212/35. Let's look at an ultra-long-term investor C. Suppose that the stock he bought with 6,543.8+0.6 million yuan has increased by 654.38+0.59 times after 26 years, reaching 6,543.8+0.6 million yuan. Then T=26 years, N=D/T = 1/26, yield K= 15900%, annualized yield y = (1+k) n-1=16065433. Suppose that after 18.3 years, only 5% of another stock bought by investor C is left, that is, the principal loss of 1 10,000 yuan is only 500 yuan, so in this investment, T= 18.3 years, n = d/t =11. It is equivalent to the annual loss of 15. 1% of the principal. Finally, let's look at an investor who can do T+0 transactions many times a day in warrants or futures markets. Suppose the market trades for 4 hours every day, and the effective trading time of one year is D=250 days ×4 hours/day ×60 minutes/hour = 60,000 minutes. Suppose he invested 1 0,000 yuan to open a position at some time one day, and closed his position after10.5 minutes, earning10.08 yuan. So in this transaction, T= 15 minutes, N=D/T=60000/ 15=4000, and the yield k =108/10000 =1.08. It is equivalent to earning 45.8 billion times a year! Therefore, the shorter the trading time, even if the absolute return of a single income is small, the annualized rate of return is very, very large, which often becomes astronomical! And if he loses 76 yuan in the principal of 1 0,000 yuan in 37 minutes in another transaction, then this time T=37 minutes, n = d/t = 60,000/37 ≈1621.62, and the yield is K=-0.76%. How to calculate the situation of multiple investments? It's actually the same. Assuming that the investor has made n consecutive investments from the principal C, the situation of the first investment (i= 1~n) is exactly the same as the above single investment, which can be specifically expressed as follows: the initial principal of the first investment is Ci, the market value at the end of the period is Vi, the time spent is Ti, the net income of this investment is Pi=Vi-Ci, and its rate of return is KI = PI/CI. Without increasing or decreasing investment funds, it is obvious that the market value at the end of each investment is equal to the initial principal of the next investment, that is, Vi=Ci+ 1. The principal of the first investment is C1= C. After all the N investments are completed, the net income P is equal to the sum of the income of each investment, that is, P=∑Pi, and the investment time is equal to the sum of the time of each investment, that is, T=∑Ti, and the investment income K = ∏ (KI+1)-/kloc-0. Then the results of all n investments are regarded as one investment, and the annualized rate of return of all n investments in this period can be simply calculated by using the calculation method of one-time investment introduced above. For example, suppose that the investor's initial investment is 10000 yuan, and he earns 50% in three months 1 time, and the account value increases to 15000 yuan; Followed by the second loss of 40% in two months, the account shrank to 0.9 million yuan; Then in the third eight months, I immediately earned 1.20%, and my account increased to 1.98 million yuan. On the whole, investors' initial 10000 yuan has increased to 19800 yuan after 13 months, and its net income is P = 09800 yuan, the yield is K=98%, and the annualized rate of return is y = (1+k). Please note that the net income of each investment here is 0.5 million yuan, -0.6 million yuan and 6.5438+0.08 million yuan respectively, and its total income is the sum of the three, 0.98 million yuan. At the same time, the three yields are 50%, -40% and 120% respectively, and the total yield is k = ∏ (ki+1)-1=1.5× 0.6× 2.2-/kloc-0. That is to say, if the sum of multiple investments is calculated as one investment without increasing or decreasing the principal, the result is no different from that of calculating each investment separately and then synthesizing it. Of course, the former is a very simple method! In the above example, if the three investments are discontinuous and there are idle funds in the middle, for example, after the first sale, the bears are 3.7 months, and the after-tax interest during the period is 18.62 yuan, while after the second investment, the bears are 2.5 months before the third investment, and the after-tax interest during the period is 7.55 yuan. How to calculate it? ! It looks complicated, but it's actually very simple! It is entirely possible to deposit two short positions in the bank as two investments to earn current interest. In this way, together with the above three investments, isn't it a five-time investment? Generally speaking, isn't the principal of10,000 yuan increased to 19826. 17 yuan after13.7+2.5 =19.2 months? The yield is K=98.26 17%, while the annualized yield is y = (1+k) n-1=1.98261712//kloc-. In fact, even if there is no interest, such as lending money to friends for a period of time, there is no interest. In short, as long as the total income k and time t in an investigation period are brought into the company formula Y = (1+k) n-1= (1+k) d/t-1. How to calculate the investment principal when it changes? Open-end fund is a typical example. Due to customers' subscription or redemption, its investment capital is constantly changing every day. At this time, although the final net income must be equal to the sum of net income in each period, that is, P=∑Pi, the investment time is equal to the sum of investment time in each continuous period, that is, T=∑Ti. However, due to the continuous increase and decrease of investment principal, the market value at the end of each period is not equal to the initial principal of the next period, that is, Vi≠Ci+ 1. In this case, there are two ways to calculate the annualized rate of return. The first method is the geometric average method, that is, first calculate the rate of return Ki for each continuous period, then calculate the total rate of return k according to the total rate of return K=∏(Ki+ 1)- 1, and then substitute it into the formula Y = (1+K) n-660. In the case of substantial changes in principal, this method can fairly and accurately examine and compare the income level of investors. However, if the principal changes little, directly substitute the initial principal C and the total net income P into the formula Y = (V/C) n-1= (V/C) d/t-1to calculate, which is essentially simplified to the case that the principal remains unchanged. Finally, summarize the quantitative formula: investors put the principal C into the market and its market value becomes V after time t, then this investment: 1, return =V-C 2, yield: K=P/C=(V-C)/C=V/C- 1 3, annualized rate of return: (/kloc) Y = ( 1+K) N-660。 D stands for the effective investment time of one year, with bank deposits, bills and bonds being D=360 days, stocks and futures being 250 days, and real estate and industry being D=365 days. 4. In the case of continuous multi-period investment, y = (1+k) n-1= (1+k) d/t-1,where: k = ∏ (ki+1.