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β coefficient and hedging ratio

The first of the four basic principles of hedging is "the principle of the same or similar varieties". Let's take a look at the first two cases.

the first case is that a securities investment institution holds a stock portfolio of 3 constituent stocks in Shanghai and Shenzhen with a market value of 2 million yuan, and it can be said that the futures contract of 3 stock indexes in Shanghai and Shenzhen is a perfect hedging tool.

in the second case, an investor is going to set up a stock portfolio of 5 constituent stocks of SSE with a value of 5 million yuan, and the futures contract of SSE 5 stock index just matches it perfectly.

Smart readers may immediately realize what to do if the objects to be hedged are different from the stock index futures? For example, if you have a portfolio of 4 stocks, although they are all constituent stocks of the Shanghai and Shenzhen 3 Index, the fluctuation range of this stock portfolio is probably different from that of the Shanghai and Shenzhen 3 Index! Maybe the Shanghai and Shenzhen 3 index rose by 1%, and that stock portfolio rose by 15%. What should I do at this time?

the common solution to this problem is quantity adjustment. For stock index futures, the method of determining the number of hedging contracts is different from that of commodity futures, and the calculation formula is as follows:

The number of stock index futures contracts required for hedging = hedging ratio × (total market value futures contract price held/contract multiplier)

The hedging ratio is the ratio between futures contract positions held and spot portfolio positions, which is the key to affect the hedging effect. After analysis and deduction, the best alternative index of the optimal hedging ratio of stock index futures is the β coefficient of stocks or stock combinations.

so what is the β(Beta) coefficient? It is a main parameter in the capital asset pricing model, which can be used to evaluate the systemic risk of securities and to measure the volatility of an asset portfolio relative to the overall market.

when β=1, it means that the asset portfolio is in step with the market changes and the risk is equivalent.

when β> 1, it means that the fluctuation range of the portfolio is greater than the overall change of the market, and the risk is higher than the whole market.

When β

When the total market value of the stock is determined, the smaller the β coefficient, the less futures contracts investors need; Conversely, the greater the β coefficient, the more futures contracts investors need.

the value of β coefficient is calculated by econometric analysis model based on the historical data of stock and index. Because there are many mathematical formulas involved, I won't expand them here. Interested and capable readers can learn from relevant financial books.

Case

On June 11, 218, the position of a stock portfolio held by an investor is shown in Table 1. According to the opening price of the day, the total market value of the stock portfolio totaled 31.95 million yuan. Since the beginning of 218, the overall performance of the A-share market has been poor, mainly due to domestic financial deleveraging, and the Sino-US trade war has also brought huge panic to investors. In the face of systemic risks, stock investors who lack hedging tools suffer heavy losses.

Table 1 Stock Portfolio Positions

Because I was worried about the decline in the market outlook, I chose to sell the hedging strategy, that is, hold the stock and short the stock index futures. In this case, on June 11, 218, the total market value of the stock portfolio totaled 31.95 million yuan, and the opening price of IF187 was 3,754.2 points. According to the weighted average of the beta value of each stock in the stock portfolio, the beta value of the portfolio is about 1.12. From this, the number of IF187 contracts that the investor needs to sell in the futures market can be calculated.

The number of IF187 sold = (1.12× 31.95 million yuan)/(3,754.2× 3 yuan/point) =31 (Zhang)

On July 6, 218, the first round of Sino-US trade war "boots" landed, the Shanghai and Shenzhen 3 Index stopped falling and stabilized, and the market panic weakened. The investor chose to end the set. By the close of July 6th, the total market value of the stock portfolio held by this investor was 27.933 million yuan, of which the market values of China Merchants Bank, CITIC Securities, Wuliangye and Minmetals were 12.51 million yuan, 4.731 million yuan, 7.62 million yuan and 3.63 million yuan respectively.

as can be seen from table 2, from June 11, 218 to July 6, 218, the stock market experienced a significant decline. If hedging is not carried out, the investor's stock portfolio will suffer a large loss. However, by using stock index futures to sell hedging transactions, the investor makes a profit in the futures market, thus successfully avoiding the risk brought by the price drop faced by the position portfolio in the stock market.

table 2 effect of selling hedging

B

risk of hedging

stock index futures hedging is an effective tool to avoid systemic risks in the stock market, but it does not mean that hedging has no risks at all. In the whole actual operation of hedging, there are not only some conventional risks, but also some new risks, such as basis risk and cross-hedging risk. Therefore, investors need to dynamically monitor all kinds of risks in hedging transactions.

basis risk

basis risk is the main factor affecting the effect of hedging transactions. Basis refers to the difference between spot price and futures price, that is, basis = spot price-futures price. Theoretically, the basis is convergent, and tends to zero as the delivery period approaches. However, if the hedging period is inconsistent with the maturity date of the futures contract, there is basis risk.

if the basis at the end of hedging is larger than the basis at the beginning, that is, the basis is stronger, the cost of buying stocks or the value of stock positions in the future will be higher than the stock price level when hedging is opened, so it is beneficial to selling hedging and unfavorable to buying hedging. On the other hand, if the basis at the end of hedging is smaller than the basis at the beginning, that is, the basis is weaker, and the cost of buying stocks or the value of stock positions in the future is lower than the stock price level when hedging is opened, so it is beneficial to buying hedging and unfavorable to selling hedging. In order to avoid the basis risk, in actual hedging, we should try our best to keep the hedging period consistent with or close to the maturity date of the futures contract. Generally speaking, the maturity date of futures contracts should be in the latest delivery month after the hedging period.

cross hedging risk

The subject matter of stock index futures is the stock price index. Only by buying and selling index funds or buying and selling a basket of stocks in strict accordance with the composition of the index can it be completely hedged. In the actual operation process, the assets that investors want to preserve are often not exactly the same as the underlying assets of stock index futures. For example, due to the limited amount of funds, it is difficult for individual investors to simulate index holdings. The stocks they hold are usually some stocks in CSI 3, SSE 5 or CSI 5, while stock index futures are short or long on the whole index. Therefore, the price trends of the two types of assets are not completely consistent, which leads to the risk of cross-hedging. Although β coefficient can be used for adjustment, it should be noted that β coefficient is also an analog value of historical data, and it is very difficult to achieve the purpose of complete hedging.

Risk of forced liquidation

As the stock index futures trading adopts the settlement system on the same day, investors may be required to make up the margin to the specified level when future positions loses money. If in the process of hedging, investors cannot make up the margin in time due to insufficient capital turnover, some or even all contracts may be forced to close their positions, and the hedging strategy will fail, and investors may face greater risks. Therefore, investors should fully estimate the amount of margin for changes in stock index futures and prepare spare funds.