What is the Difference Between Interest Rate and Annual Percentage Yield?

The annualized rate of return is calculated by converting the current rate of return (daily rate of return, weekly rate of return, and monthly rate of return) into an annual rate of return. It is a theoretical rate of return and is not a real rate of return.

Annualized rate of return

Annualized return is investment

The annual rate of return is the ratio of the actual annual return on an investment.
The annualized rate of return is the return of the investment (commonly used by money funds) over a period of time (such as 7 days). It is assumed that the year is at this level, and the converted annual rate of return. Because the annualized rate of return is changing, the annual rate of return may not be the same as

For example, a financial product sold by a bank claims to have an annualized return of 3.1% in 91 days. Then you purchase 100,000 yuan. In fact, the interest you receive is 100,000 * 3.1% * 91/365 = 772.88 Yuan, definitely not 3100 Yuan. It should also be noted that the wealth management products of ordinary banks are not the same as that of banks on a regular basis.

Annualized rate of return quantitative formula

Summary: The investor invests the principal C in the market and its market value becomes V after time T. In this investment:

1. The income is: P = VC

2. Yield: K = P / C = (VC) / C = V / C-1

3. Annualized return rate:

(1) Y = (1 + K) ^ N-1 = (1 + K) ^ (D / T) -1 or

(2) Y = (V / C) ^ N-1 = (V / C) ^ (D / T) -1

Where N = D / T represents the number of repeated investments made by an investor within a year. D represents the effective investment time for one year, D = 360 days for bank deposits, bills, bonds, etc., D = 250 days for stocks and futures markets, and D = 365 days for real estate and industry.

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

Annualized rate of return conclusion

How to calculate the annualized rate of return? Let's start with a simple example: a one-time investment. Assume that the investor has invested 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 T, then the investor's gain (or loss, if V <C) during this period Is P = VC, and the rate of return (that is, the absolute rate of return, hereinafter referred to as the rate of return) is K = P / C = (VC) / C = V / C-1, and assuming that all effective investment time in a year is D, The number of times an investor can make repeated investments in a year is N = D / T, then the annualized return on the investment can be expressed as: Y = (1 + K) ^ N-1 = (1 + K) ^ (D / T) -1 or Y = (V / C) ^ N-1 = (V / C) ^ (D / T) -1.

Here, the effective investment time D for one year varies with different markets. Interests such as bank deposits, bills, bonds, etc. are generally calculated every 360 days (or 365 days in rare cases), that is, D = 360 days. For public trading 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 holidays (52 weeks per year, 5 trading days per week, and about 10 days a year. Holidays: 52 × 5 -10 = 250) or D = 250 days. For real estate, general business, industry, etc., because they can be bought or sold every day and are not affected by holidays, the effective investment time is the natural number of days in a year, that is, D = 365 days. Very special circumstances, such as an extra day in an individual year due to a leap year, are of negligible nature because of its small impact.

Annualized rate of return case

For example, suppose that investor A invests 10,000 yuan (C = 10,000 yuan), and after one month the market value increases to 11,000 yuan (V = 11,000 yuan), then the return is P = VC = 10,000 yuan, That is 1,000 yuan. Then the return on this investment is K = P / C = 10%. Since there are 12 months in a year, that is, the same investment can be repeated 12 times a year (N = D / T = 12), so its annualization The yield is Y = (1 + K) ^ 12-1 = 1.1 ^ 12-1213.84%. That is, earning 10% a month is equivalent to 2.1384 times a year. If investor A repeatedly invests in this way, the principal of 10,000 yuan can be added to 31,384 yuan in one year.

Conversely, if the investor is unfortunately losing 1,000 yuan a month, the net income of the investment is P = -0.1 million, the yield is K = P / C = -10%, and the annualized return is Y = (1 + K) ^ 12-1 = 0.9 ^ 12-1-71.76%. That is to say, if the investor loses 10% every month, 71.76% of the principal will be lost after one year, and by the end of the year, there will be only 2824 yuan in the principal of 10,000 yuan.

What if I make 10% a day? For example, the stock bought at the closing price yesterday was very lucky to have made a daily limit, so how high is the annualized rate of return? Here it is clear that the yield K = 10%, and the number of days in a year when the investment can be repeated is the number of trading days in a year, which is N = 250. Therefore, the annualized return is Y = (1 + K) ^ N-1 = 1.1 ^ 250-1 2.2293 × 10 ^ 10, which is 22.293 billion times! That is to say, if the investor makes a daily limit, the initial 10,000 yuan principal can be added to 222.93 trillion yuan in one year! What a rich country! !!

Conversely, if the investor unfortunately encounters a limit stop, the return rate is K = -10%, and the annualized return rate is Y = (1 + K) ^ 250-1 = 0.9 ^ 250-13.636 × 10 ^ ( -12) -1 -1 = -100%. Obviously all the investors' principal losses have been completed!

Let's look at the second example. Investor B did a long-term and earned 3.6 times in 28 months, that is, the initial investment of 10,000 yuan was increased to 46,000 yuan in two years and 4 months. The investment time for this investment is T = 28 months, so the number of times that it can repeat investment each year is N = D / T = 12/28. The return on this investment is K = 360%, and the annualized return is Y = (1 + K) ^ N-1 = 4.6 ^ (12/28) -192.33%, which is close to doubling every year. .

If investor B's second long-term investment is a loss of 68% in 35 months, that is, the original investment of 10,000 yuan in the principal 2 years and only 11 months left only 3,200 yuan. Then the time of this investment is T = 35 months, N = D / T = 12/35, and the return rate K = -68%, then the annualized return rate Y = (1 + K) ^ N-1 = 0.32 ^ (12/35) -1-32.34%, which is close to 1/3 of the annual loss.

Let's look at an ultra-long-term investor C. Suppose that the stock he bought after investing 10,000 yuan increased in value by 159 times to 1.6 million yuan 26 years later. Then in this investment, T = 26 years, N = D / T = 1/26, return rate K = 15900%, and annualized return rate Y = (1 + K) ^ N-1 = 160 ^ (1 / 26) -1 = 21.55%, which means that its investment level is comparable to another investor who earns 21.55% a year.

Suppose that the other stock that investor C initially bought has only 5% after 18.3 years, that is, the principal loss of 10,000 yuan to only 500 yuan, then T = 18.3 years in this investment, N = D / T = 1 / 18.3, the return rate K = -95%, and the annualized return rate is: Y = (1 + K) ^ N-1 = 0.05 ^ (1 / 18.3) -1-15.1%. That is equivalent to a loss of 15.1% of the principal each year.

Finally, let's look at an investor D who can make multiple T + 0 transactions per day in the market such as warrants or futures. Assume that the market trades for 4 hours a day, and the effective trading time for a year is D = 250 days × 4 hours / day × 60 minutes / hour = 60,000 minutes. Suppose he invested 10,000 yuan to open a position at a certain time and some day, and closed the position 15 minutes later and made 108 yuan. Then in this transaction, T = 15 minutes, N = D / T = 60000/15 = 4000, yield K = 108/10000 = 1.08%, then the annualized yield is Y = (1 + K) ^ N-1 = 1.0108 ^ 4000-14.58 × 10 ^ 18! This is equivalent to making 45.8 billion times a year! It can be seen that the shorter the transaction time, even if the absolute return of a single return is small, the annualized return is very, very large, and often becomes an astronomical number! And if he lost 76 yuan in 10,000 yuan in 37 minutes in another transaction, then this time T = 37 minutes, N = D / T = 60000 / 371621.62, and the yield K = -0.76% The rate of return is Y = (1 + K) ^ N-1 = 0.9924 ^ 1621.62-10-1 = -100%.

How to calculate the situation of multiple investments? It's actually the same. Suppose that the investor started with the principal C and made n consecutive investments, then the situation of the i-th (i = 1 n) investment is exactly the same as the single investment described above, which can be specifically expressed as: The initial principal is Ci, the closing market value is Vi, and the elapsed time is Ti. The net income of this investment is Pi = Vi-Ci, and the rate of return is Ki = Pi / Ci = (Vi-Ci) / Ci = Vi / Ci-1. In the absence of additional or reduced investment funds, it is clear that the closing market value of each investment is equal to the opening principal of the next investment, ie, Vi = Ci + 1. The principal of the first investment is C1 = C. After all n investments are completed, the net income P is equal to the sum of the returns of each investment, ie P = Pi, the investment time is equal to the sum of the times of each investment, ie T = Ti, and the investment income K = (Ki + 1) -1. The results of all n investments are then regarded as one investment. Using the one-time investment calculation method described above, the annualized rate of return of all n investments during that period can be simply calculated.

For example, suppose that an investor initially invests 10,000 yuan in principal, earns 50% in the first 3 months, and the account value increases to 15,000 yuan; then the second two months lose 40% of the account and the account shrinks to 0.9 10,000 yuan; then immediately earned 120% for the third eight months, and the account value increased to 19,800 yuan. On the whole, the investor's initial 10,000 yuan increased in value to 19,800 yuan after 13 months. Its net income was P = 0.98 million, the yield was K = 98%, and the annualized yield was Y = ( 1 + K) ^ N-1 = 1.98 ^ (12/13) -187.87%. Please note that the net income of each investment here is 50 thousand yuan, -60 thousand yuan and 10,800 yuan, and the total income is the sum of the three, which is 0.98 million yuan. At the same time, the three returns are 50%, -40%, and 120%, and their total returns are K = (Ki + 1) -1 = 1.5 × 0.6 × 2.2-1 = 98%. That is to say, in the case of neither adding nor reducing the principal, the total of multiple investments is regarded as one investment to calculate, and the result is no different from calculating each investment separately and then recombining, of course, in comparison The former is a very simple method!

In the above example, if the three investments are not continuous and there are funds in the middle, for example, the short position after the first sale is 3.7 months, during which the interest after tax is 18.62 yuan, and after the second investment is in the third Before the second investment, it was shorted for another 2.5 months. During the period, the interest after tax was 7.55 yuan. How should it be calculated? !! It looks complicated, but it's actually very simple! It is entirely possible to treat two short positions as the other two deposits for the bank to earn current interest investment. In this way, plus the above three investments, will not it become five consecutive investments? In general, isn't it that the principal of 10,000 yuan has increased to RMB 19,826.17 after 19.2 months (13 + 3.7 + 2.5 = 19.2)? In this way, the return rate K = 98.2617%, and the annualized return rate Y = (1 + K) ^ N-1 = 1.982617 ^ (12 / 19.2) -1 53.38%.

In fact, even if there is no interest in the middle, such as lending money to a friend without interest for a period of time and then recovering it, it is still the same. In short, as long as the total return K and time T for a period of investigation are brought into the formula Y = (1 + K) ^ N-1 = (1 + K) ^ (D / T) -1.

In the case of changes in investment principal, how to calculate it? Open-ended funds are a typical example. The amount of investment funds affected by customers' purchases or redemptions changes continuously every day. At this time, although the final net income must also be equal to the sum of the net income of each time, that is, P = Pi, the investment time is equal to the sum of the time of each successive investment, that is, T = Ti. However, due to the continuous increase or decrease of the investment principal, the market capitalization at the end of each period is not equal to the capital at the beginning of the next period, ie Vi Ci + 1. In this case, there are two methods to calculate the annualized rate of return. The first is the geometric average method, that is, first calculate the continuous rate of return Ki, and then based on the total rate of return K = (Ki + 1 ) -1 to calculate the total rate of return K, and then substitute the formula Y = (1 + K) ^ N-1 = (1 + K) ^ (D / T) -1 to calculate. In the case of large changes in principal, this method can be used to fairly and accurately examine and compare the level of investor returns. In the case where the principal fluctuation range is not very large, the initial principal C and the total net income P are directly substituted into the formula Y = (V / C) ^ N-1 = (V / C) ^ (D / T ) -1 can be calculated, its essence is to simplify it to the case of no principal change.