**Guide**

Fixed investment is a simple and effective investment method. Some researchers said, "No matter how volatile the price of securities, this investment method can make investors full of confidence. So far, there is no investment law comparable to the dollar average cost method."

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Fixed investment, that is, regular fixed investment. This type of investment includes two aspects of “fixing”: regular and fixed. Regularly means that the time interval between each occurrence of investment behavior is fixed, and the quota refers to the fixed amount of each time the asset used to purchase the investment target is fixed. In addition to regular and fixed quotas, the characteristics of fixed investment include: batch investment and investment target are mostly risk assets.

The advantages of fixed investment are: reduce the average cost of purchasing assets; match the cash flow of investors; reduce the requirement for timing ability. Fixed investment is a more defensive investment strategy for stable and entry-level investors. There are more investors in the digital pass market, which is suitable for a fixed investment strategy. The shortcoming of the digital pass is that the price brought by the exchange is not uniform and the income calculation is inconvenient.

We choose three typical market conditions: the starting point of the bull market, the peak of the bull market, and the shock market. We use the BTC historical data backtest to conduct empirical research, and compare fixed investment with one-time investment. The starting point of the bull market: precise timing, should be a one-time investment; the bull market apex: expected long-term security, suitable for fixed investment; shock down the beginning: should adopt a fixed investment strategy. The current digital pass market is suitable for fixed investment.

Risk warning: market fluctuation risk.

**table of Contents**

1 General rules and their characteristics

1.1 What is a fixed vote?

1.2 The "smile curve" of the fixed vote

1.3 Fixed investment matches investor cash flow

1.4 Fixed investment to reduce the requirement for timing ability

1.5 Is the digital pass suitable for a fixed vote?

2 Empirical research on fixed investment strategy

2.1 Research on the starting point of the bull market – a precise one, a one-time investment

2.2 The study of the bull market's apex investment – it is better to be fixed in the long-term

2.3 Research on the market's fixed investment

3 The current market should adopt a fixed investment strategy

3.1 Advantages of fixed investment in the current market environment

3.2 Target selection for the investment

3.3 Determination of the frequency of fixed investment

4 The theoretical basis of fixed investment

4.1 Fixed Cash Flow Model and Income Calculation

4.2 Principle of fixed investment to reduce average cost

4.3 Assets with higher volatility are suitable for fixed investment

**text**

"Many human happiness is mostly not from rare luck, but from a little bit of daily income." – Benjamin Franklin

## **1** **pass certificate and its characteristics**

**1.1 What is a fixed vote?**

Fixed investment, that is, regular fixed investment. Graham mentioned "the dollar cost averaging method" in "Smart Investors": The New York Stock Exchange promotes the "Monthly Purchase Plan", in which investors invest the same amount of money each month to buy one or more stocks. Lucile Tomlinson conducted a comprehensive study of this stylized investment. She used the Dow Jones Industrial Index constituents as a sample, covering the price data of 1929-1952, and came to the following conclusion: "No matter how volatile the price of securities, this kind of Investment law can make investors full of confidence. So far, there is no investment law comparable to the dollar average cost method."

After more than half a century of Graham's writings, fixed investment (also known as automatic investment planning, AIP) has become an important investment tool. The trading strategy used is still the investment cost averaging method. Trading orders are generally issued by pre-set rules. . This type of investment includes two aspects of “fixing”: regular and fixed.

Regularly means that the time interval between each occurrence of investment behavior is fixed. There are usually different periods of weekly, bi-weekly, natural-monthly, quarterly, etc., depending on the investor's cash flow characteristics or investment preferences.

Quota refers to the fixed amount of the asset used to purchase the investment target each time. Since the price of the target asset fluctuates when each investment occurs, the amount of assets purchased in each investment is also different. When the price of an asset rises, the amount of the purchased asset decreases; on the contrary, when the price falls, the amount of the purchase increases, thereby achieving the goal of lowering the average cost.

In addition to regular and fixed terms, the characteristics of fixed investment include:

Invest in batches. Regular investment implies the concept of “fractionation”, in which investors’ funds are not used to purchase target assets at one time. Even if investors do not have stable cash flow income, but hold a certain amount of principal, they can adopt a strategy of regular batch investment.

Most of the investment targets are risk assets such as stocks, stock funds, and indices. If investors regularly buy wealth management products such as bonds and money funds that are less volatile and have low risks, then it is not necessary to use the fixed investment strategy. Because the advantage of fixed investment is to buy assets with large fluctuations at a lower average price.

**1.2 The "smile curve" of the fixed vote**

The biggest advantage of fixed investment compared to other long-term investment strategies is that it can reduce the average cost of purchasing assets. The “smile curve” of fixed investment is widely known. When the market shows a wave of declines and then rises, the yield curve of the fixed investment strategy will form a smile-like shape. The longer the downswing lasts, the more time there is to spend on lower-priced purchases and dilute costs. When the market starts to pick up, it can be profitable as long as the price exceeds the average cost.

The following is an example of the 32-month BTC historical price from November 2013 to July 2016. The average cost and profit rate of the weekly investment and the initial one-time investment in the selected time period are compared.

**1.3 Fixed investment matches investor cash flow**

Fixed investment is suitable for investors with stable cash flow income. For example, investors can use a portion of their monthly income for a fixed investment. The benefits are: the amount of investment matches its own income and budget, even if the investment losses, it will not let investors fall into bankruptcy crisis; use idle money to invest, reduce the psychological burden of investors when losses occur; long investment cycle, able to Crossing the bulls and bears, effectively reducing investment costs and improving the efficiency of capital utilization during the bear market.

Even investors who have a certain principal and do not have a stable cash flow can adopt a fixed investment approach. Short-term financial management with a stable rate of return, such as a monetary fund, can be redeemed for a fixed amount at the planned time and used for fixed investment.

**1.4 Fixed investment to reduce the requirement for timing ability**

"Time-making" refers to the choice of trading points through basic or technical analysis. For ordinary investors, there is no long-term investment experience, and it is difficult to grasp the timing judgment. The fixed investment can be effectively reduced by selecting a single investment for a long period of time, which can effectively reduce the risk of “entry timing”.

If the investor's entry time is poor, when the first purchase, the price of the asset will start to fall, and the subsequent fixed investment will allow investors to buy more assets at a lower price, thus reducing the average cost. .

In contrast to investors who do not have the ability to make time, assuming that the buying opportunity is a random variable distributed over a period of time, then the expected cost is the arithmetic mean of the price during that time. Comparing the average cost of a fixed investment with the expected cost of a one-time investment by an untimely ability investor, it can be concluded that the fixed investment cost is always better than the expected cost of a one-time investment.

When the fixed investment takes longer, the average cost is also affected by the change in the impact of each new investment. Therefore, the long-term profitability of fixed investment depends more on the price of assets at the time of exit, that is, more attention is paid to the timing of selling and whether the assets are of high quality.

However, in a unilaterally rising market, the profitability of a fixed investment may not be as good as a one-time investment at the beginning of the period. In the market that fell first and then fell, the fixed investment will continue to raise the average cost. When the asset price is lower than the average cost of fixed investment, it is the most efficient period for investors to use.

All in all, fixed investment is a more defensive investment strategy for stable and entry-level investors.

**1.5 Is the digital pass suitable for a fixed vote?**

The investment targets of fixed investment are mostly risk assets with large volatility, and the specific reasons will be analyzed later. At present, the mainstream fixed-term wealth management products in the market include fund-based investment and stock-specific investment. With the booming development of the blockchain industry and the digital passbook secondary market, digital certificates such as BTC and ETH have gradually entered the field of traditional investors.

However, the current professional ability of digital pass investors is not as good as traditional investors. The threshold for digital pass is low, and the entry investors also have shortcomings in terms of trading philosophy, strategy, and execution. As a procedural and defensive investment strategy, fixed investment can effectively prevent investors from investing all the principal in the wrong time. The resulting losses are suitable for investors who are not sure about the timing of entry and prepare for long-term investment. They have a high probability of making profits and reducing risks. The target of the investment may choose a certain pass or a fund that tracks the blockchain index.

The shortcomings of the current Compulsory Fixed Investment include that there is a price difference between the exchanges of different exchanges, and there is no mainstream industry index and corresponding tracking fund in the current market, so that the purchase of the certificate, the determination of the purchase share, the calculation of the income, etc. There is a certain inconvenience.

## **2 Empirical research on fixed investment strategy**

In the general market, BTC has the longest history, the highest market share, the strongest consensus, and experienced a complete two-cycle cycle. So in the empirical study we used BTC for analysis.

Similar to most other assets, the choice of entry time has a greater impact on the rate of return for the fixed investment, and investors have a large discretion on when to enter. Therefore, we select three typical entry time points and analyze the impact of one-time investment and fixed investment strategy on the rate of return.

Due to the doubts about the reliability of BTC's early transaction data, we took the second round of the bull market peak in November 2013 as the starting point for the study, and set the end point to January 24, 2019.

**2.1 Research on the starting point of the bull market – a precise one, a one-time investment**

If a trader makes a one-time investment in the starting point of the third round of bull market and has been holding it until now, the yield will be greater than the fixed investment strategy. The third round of the BTC price cycle has not yet fully completed, and is currently in the downward phase of the price cycle of this round of price cycles. The price increase of this round cycle started from August 2015 and lasted for 845 days in December 2017. The starting price of the price up cycle BTC was US$199.57/piece, and the highest price was close to US$20,000/piece. Up to 99 times. Since December 2017, the price of this round has started to decline. So far, the lowest drop has hit $3,200, a drop of 84%.

If the trader buys BTC in the whole position at 00:00 on August 25, 2015 and holds it, the BTC holding cost is $221.60 per piece. Since then, BTC has never fallen below this price. Therefore, the decision of the investment strategy is The function of low average cost is not only impossible to take effect, but will increase the cost of holding positions. As of February 22, 2019, the BTC price was $4005 per piece, and its yield was approximately 2047%.

However, if the trader chooses to start a 30-day fixed-term investment plan on August 25, 2015, then the BTC holding cost after the 42-point fixed investment is $869/piece, which is much higher than the $221.60/piece. Sexual investment cost line. After several rounds of fixed investment, as the cost line of positions was significantly increased, as of February 22, 2019, the yield of the fixed investment plan was only 343%.

**2.2 The study of the bull market's apex investment – it is better to be fixed in the long-term**

If investors enter the market at the peak of the second round of bull market, a one-time investment will make it a long-term floating state. The fixed investment will reduce the time of floating loss and the average position cost. The return rate of fixed investment will also be higher than the one-time investment. From November 2011 to November 2013, it was the price up cycle of the second round of price cycles, lasting 743 days. In this price up cycle, the starting price of BTC was $1.99 per piece, and the highest price was $1,242. / piece, the increase rate reached 623 times. From November 2013 to August 2015, it is the price down cycle phase of the second round of price cycle, lasting 634 days. In this price down cycle, the starting price of BTC is $1,242 per piece, and the lowest price is $199.57. / piece, a drop of 84%.

If the investor buys BTC at 00:00 on November 30, 2013 at 00:00, the investor will have to endure the floating loss period of more than three years at a position cost of $1,129 per piece. In the past three years, the BTC dropped to a minimum of $199.57 per piece, which means that the maximum withdrawal of the investment reached 84%. As of January 24, 2019, the investment income was 218%. During the investment period, he experienced a three-year floating loss, twice more than 80% retracement, and multiple times. Regardless of the rate of return, in the process of investing in BTC, if the account cannot be operated due to objective reasons such as forgetting his or her private key, the value of the spiritual experience obtained must be greater than the yield of 218%.

On the contrary, if the investor opens an interval of 30 days at 00:00 on November 30, 2013, the situation will be much better. With the decline in BTC prices, the implementation of the fixed investment plan has led to a rapid decline in position costs. After 38 rounds of fixed investment, the cost of holding positions fell to a minimum of $347.63 per piece on November 21, 2015. In November 2015, the yield of the fixed investment plan was positive for the first time. Although the investor still needs to endure the two-year floating loss, its maximum retracement is much lower than the one-time input, which is 65%, and the duration of the sharp retracement is shorter. Taking into account the discipline and rules of the implementation of the fixed investment plan, the investor who chooses to vote for the investment in the four years after the start of the fixed investment, the psychological pressure will be significantly smaller than the investor who stood at the peak for three years. As of February 22, 2019, the fixed-income plan had a yield of 548%, which was significantly better than the one-time investment yield of 254%.

Comparing the profit and loss time of the two investment methods, it can be found that at the same time, the investment plan is started, and the number of days of fixed investment losses is far lower than the one-time investment. This is due to the bullish apex of the bull market to start a fixed vote on the average price of the position.

**2.3 Research on the market's fixed investment**

In most cases, it is difficult for investors to accurately check the bottom, and it is difficult to buy accurately at the peak of the bull market, usually entering the market in a volatile market. Therefore, we analyzed the historical price of BTC from May 23, 2017 to February 22, 2019, and calculated the cumulative income of the two strategies of fixed investment and one-time investment each day as of February 22, 2019. Some conclusions were drawn.

First of all, it is suitable to adopt a fixed investment strategy in the market where the shock has just started. Between March 2018 and November 2018, BTC prices were generally in a down state. If a fixed-term investment plan with a 30-day interval is started during this time, the investment results are better than the one-time investment. During this time, the BTC price showed a downward trend. At this moment, the fixed investment will play one of the biggest advantages of the fixed investment – lowering the average position cost.

As shown in the figure, starting the fixed investment plan in this interval and insisting on February 22, 2019, the investor's position cost will be lower than the one-time buy and hold strategy position cost on the start date of the fixed investment. In terms of yield, it is also advisable to start a investment plan during this period. Due to the decline in the cost of holding positions, the maximum withdrawal rate and duration of fixed investment is also much less than that of one-time investors.

Secondly, in the late stage of the shockdown phase, the decline began to ease, and after the BTC price has already produced a large decline, a one-time investment strategy should be adopted. After December 2018, BTC has fallen from the peak of the bull market to most of the market value. Although it is in the down phase of the shock, it is not effective to adopt a fixed investment strategy during this period. There are two reasons for this. First, the core of the fixed investment – the batch-based fixed purchase is a double-edged sword. In the market of shocks, this double-edged sword will lower the average position cost, and in the shock In the market, it will raise the average cost of holding positions; secondly, there is not much room for prices to continue to fall, which makes the advantage of fixed investment – the role of reducing costs has a limited effect.

Finally, in a market that is oscillating upwards, it is suitable for a one-time investment strategy. In the early period of the bull market, the price of BTC fluctuated upwards. At any point in this phase, the fixed investment will continue to increase the cost of holding positions. On the other hand, a one-time investment is made on any day of this stage. As long as the start time of the two is the same, there is no advantage worth mentioning in the one-off investment.

## **3 The current market should adopt a fixed investment strategy**

**3.1 Advantages of fixed investment in the current market environment**

First, the fixed investment can match the cash flow and is suitable for young investors.

The fixed investment strategy can match the cash flow. In general, young investors tend to invest in risky assets such as BTC. Although there is not much savings, they have a gradual increase in income expectations. Regularly using part of the income for BTC investment will not affect the quality of life, but will increase hope for future life. In addition, if we look at this investment plan on a yearly scale, long-term investment in a fast-growing new asset is likely to give young investors an early financial freedom.

Secondly, the ability of fixed investment is not high, but the effect is even better than subjective timing.

The investment strategy does not need to be timed, suitable for investors who do not have the energy to stare daily. The trading market is open 24 hours a day, and individual investors are hard to achieve good investment results due to limited energy and funds. Moreover, the current market is in the late bear market, the market value has shrunk dramatically, liquidity has decreased, and the trend in the short term is more difficult to predict. If the price of the pass after the one-time investment continues to fall, investors will likely face great pressure. On the contrary, if a fixed investment strategy is adopted and the market continues to fall, investors can purchase more passes at a lower unit price. It would be pleasing to admit that buying assets that would rise in the future at a lower price would be pleasing, and that falling would bring negative emotions such as anxiety and remorse. Then, when the investment is fixed, the asset that will rise in the future at a cheaper price and the current temporary asset price decline will constitute a hedging relationship in the investor's sentiment, and vice versa. In this way, investors will be able to win without arrogance, avoid being passive in the volatile market, and invest in the certificate with a healthier attitude.

Most investors are non-professional traders. Due to their busy work, investors often can't give enough energy to analyze the short-term trend of BTC and make precise timing. Avenue to Jane, deriving to the complex. Instead of struggling to predict short-term trends, it is not uncomfortable to go up and down a few points. It is better to choose a low-risk investment strategy, which can enjoy the dividends brought about by the rapid development of the pass-through economy, and can also give energy to enjoy life. After all, in investing, the energy and income invested are not directly proportional.

When the price of BTC continues to fall, investors who choose to invest in one-time investment will not only generate doubts about their own decisions, but also suffer from a large number of outside doubts and multiple pressures to give up and admit defeat. Most regrettably, some investors may even fall before dawn. In fact, the pass of the circumstance tells the story of two different endings:

At the beginning of 2014, the investor who called “48 million brothers” lived in Baidu Post to broadcast the story of BTC worth 480,000 RMB in one time, and finally, under the suspicion of their own suspicions and loved ones, before June 2016. Loss clearance clearance, loss of 180,000. On the contrary, the registered owner of the Babbitt Forum “Old Captain” started the fixed investment plan on March 11, 2015, ending in February 2017. As of today, the "old captain" has a total investment of 110,000 yuan. If it does not calculate the forked coin produced by the BTC's multiple forks, its value now exceeds 1 million.

**3.2 Target selection for the investment**

BTC has a fixed investment value. The longer the history of the certificate, the more active the transaction, the stronger the consensus, and the establishment of the consensus has a strong Matthew effect. How difficult it is to build consensus and how difficult it is to eliminate consensus. Therefore, BTC is the least likely to return to zero in all passes. In addition, even in the bear market, BTC has strong liquidity, and most individual investors do not need to consider the problem of insufficient BTC funds. Although from the perspective of maximum revenue, the fixed investment BTC may not be able to vote for certain cottages. However, the above two points jointly determine that from the perspective of risk, the fixed investment BTC is far superior to the other cottages. Since the birth of the first BTC in 2009, its price has gone through three rounds. The time span of the first round of BTC price cycle was from March 2010 to November 2011, lasting 610 days, which was the largest increase in the three BTC price cycles in history. The second round of the BTC price cycle spanned from November 2011 to August 2015 and lasted for 1,377 days. At this time, the unit price of BTC exceeded gold for the first time. The third round of the BTC price cycle has not yet fully completed, and is currently in the downward phase of the price cycle of this round of price cycles. The price increase of this round cycle started from August 2015 and lasted for 845 days in December 2017. The starting price of the price up cycle BTC was US$199.57/piece, and the highest price was close to US$20,000/piece. Up to 99 times. Since December 2017, the price of this round has started to decline. So far, the lowest drop hit $3,200, a drop of 84%, and recently rebounded to around $4,000. Although the BTC has had a large decline since the apex, it is still likely to be low in the future. At this point, adopting a fixed investment strategy can reduce the possibility of buying a full position at a high point and reduce the risk of excessive cost when opening a position. The BTC is also the one that is the least likely to return to zero in all passes. Therefore, the fixed investment BTC is a good strategy for the risk-benefit ratio that is currently worth adopting.

3.3 Determination of the frequency of fixed investment

Our empirical analysis shows that (if you need detailed back-test data, please contact the General Research Institute), there is no significant difference in income between weekly and monthly investment. Investors can determine the frequency of the fixed investment based on the frequency of their own stable cash flow.

We selected BTC price data from April 8, 2013 to January 24, 2019, and adopted a fixed investment strategy on the 30th and 7th respectively. The final return on the 30th frequency is 499.8%, and the final return on the 7th frequency is 497.1%. The t-test under the assumption of the variance of the net daily value of the two found that the p value was 0.46, much larger than 0.05, showing that there was no statistically significant difference between the two.

In addition to the 30th and 7th days, we also compared a large number of frequency combinations. We found that when the total number of fixed investment periods exceeds 20, the effect of the fixed investment frequency on the final income is minimal. If the investor decides to adopt a fixed investment strategy of more than 20 periods, then it is not necessary to consider the impact of the fixed investment frequency on the yield, just match it with its own cash flow.

## **4 theoretical basis of fixed investment**

**4.1 Fixed Cash Flow Model and Income Calculation**

Annuity means receiving or paying the appropriate amount at regular intervals. By definition, a fixed investment can also be seen as an annuity. Since the investment behavior occurs at the beginning of each period, it is the beginning annuity.

For convenience, it is assumed that the number of scheduled investment is M times per year, that is, the interval between each period is 360/M day, the amount of investment per period is 1, the duration is M, and the price of the initial period of the t-term is P_t, then each period is purchased. The number of assets is Q_t=1/P_t.

After the T-term fixed investment, the number of assets held is Sigma (1/P_t), and the average cost is

At the end of the T period, the price of the asset is P_T+1. The ending (cumulative) rate of return of the fixed investment plan after the scheduled investment

Convert annualized rate of return in a simple way

If you consider the time value of the currency, you need to discount the investment for each period and the asset price at the end of the T period. Assume that the risk-free annual interest rate is r. Then the discount factor for each period is

After the T period fixed investment, the average cost discount value is

The discounted value of the asset price at the end of the period T

rate of return

In addition to simply calculating the cumulative rate of return and the annualized rate of return, taking into account the time cost of funds, we can also calculate the return of the fixed investment plan using the revised internal rate of return method (MIRR). This method discounts the investment amount of each period to the beginning of the first period at a predetermined discount rate, and discounts the discount to the end of the last period. And assume an unknown rate of return, at which the final value of the total return is discounted to the beginning of the period and equal to the discounted value of the total investment, then the rate of return is the corrected rate of return.

Here is the revised internal rate of return for annualization. The advantage of this method is that, considering the time cost, the time value of the investment amount and the reinvested return of the received return are calculated at a predetermined discount rate. This method is usually suitable for use in cash inflows such as redemption in the middle of a fixed investment. However, this method is more complicated. Generally, the time factor is not considered when comparing the returns of fixed investment, and a simple cumulative rate of return is adopted.

**4.2 Principle of fixed investment to reduce average cost**

Suppose an investor wants to invest in an asset N times in a certain period of time, and further assumes that the investor can only invest at certain fixed points in time, and the price of the asset at these points is P1, P2, P3,…, the quantity of assets purchased is Q1, Q2, Q3, …. The average cost of the investor to obtain the asset is

If the investor chooses to invest all the funds at a certain point in time, then

Where t is a random variable, and

Then the investor’s expectation of asset cost is

Is the arithmetic mean of the asset prices at these points in time.

If the investor buys the same amount of assets each time, ie Q1=Q2=…=Qn, then

Explain that the cost of this strategic investment asset is the same as the expected cost of a random purchase.

If you use the same amount of investment each time, ie Qi=1/Pi, the average cost

It is the harmonic mean of the asset prices at these points in time. Since the average of the harmonics of any positive real number is always not greater than the arithmetic mean,

Therefore, using a fixed-rate investment approach can reduce the average cost more effectively than a fixed-quantity, one-time investment.

**4.3 Assets with higher volatility are suitable for fixed investment**

In the financial world, geometric Brownian motion is often used to describe random fluctuations in stock prices. Because geometric Brownian motion has the following characteristics:

Satisfying the normal distribution can be used to describe the continuous compound interest rate of stocks.

Brownian motion is the Markov process, that is, the future price distribution is only related to the price of the current moment, and has nothing to do with the historical price. That is, the current price has fully reflected the information needed to predict future prices, in line with the weak effective market hypothesis.

The Brownian movement is continuous everywhere but not everywhere, and its secondary variation is greater than zero, in line with people's perception of stock price changes.

We assume that the return on investment in a very short period of time is in line with the geometric Brownian motion:

Where u is the expected rate of return on the asset, and o is the volatility of the asset, which is the standard deviation of the rate of return of the asset in a short period of time. W(t) is the standard Brownian motion, and its expectation is o. The expression of the difference TP(t) above the interval of length T is:

If the investor makes N fixed shots within time T, the average cost of the fixed investment is:

Assuming that the investor invests "continuously" during the time, P_D can be written as an integral form:

If the investor makes a one-time investment at time 0, the cost is P(0), comparing P_D with P(0):

The expectation of the above formula can be concluded:

The expected average cost of a fixed investment is lower than the one-time investment at the beginning of the period. That is, the higher the volatility of the asset, the lower the expected rate of return, and the fixed investment has an advantage over the one-time investment.

**Note:**

For some reasons, some of the nouns in this article are not very accurate, such as: pass, digital pass, digital currency, currency, token, Crowdsale, etc. If you have any questions, you can call us to discuss.

This article is original for the General Research Institute (ID: TokenRoll). Unauthorized reproduction is prohibited.

Text: Song Shuangjie, CFA; Sun Hanru, Analyst; Tang Wei, Intern Analyst