Quantitative formula

Summary: Investors put the principal C into the market, and its market value becomes V after time t, so in this investment:

1, and the return is: p = v-c.

2. The rate of return is: K=P/C=(V-C)/C=V/C- 1.

3. The annualized rate of return is:

(1) y = (1+k) n-1= (1+k) (d/t)-1or

(2)y=(v/c)^n- 1=(v/c)^(d/t)- 1

Where N=D/T represents the number of repeated investments by investors within one year. 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)- 1, T=∑Ti.

conclusion

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, if V,

Here, the effective investment time d of one year varies from market to 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.