股票投資與利率數學建模

❶ 股市分析的數學建模問題 求高手指點

紗布以為老子不知道你丫是西工大的？真TM丟人！用正常的數模關鍵詞搜出你們這群王八！

❷ 證券投資問題 數學建模

❸ 急急急！！！利率變動對股市影響的數學公式（數學模型也可以）

沒有公式，你看下面的信息自己做一個正反比例的模型，然後倒入這幾年的經濟數據擬合吧！！
（參考資料，英文中文都有）

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一般理論上來說,利率下降時,股票的價格就上漲；利率上升時,股票的價格就會下跌。因此,利率的高低以及利率同股票市場的關系,也成為股票投資者據以買進和賣出股票的重要依據。

利率對於股票的影響可以分成三種途徑:

一是利率變動造成的資產組合替代效應,利率變動通過影響存款收益率,投資者就會對股票和儲蓄以及債券之間做出選擇,實現資本的保值增值。

通過資產重新組合進而影響資金流向和流量,最終必然會影響到股票市場的資金供求和股票價格。利率上升,一部分資金可能從股市轉而投向銀行儲蓄和債券,從而會減少市場上的資金供應量,減少股票需求,股票價格下降；反之,利率下降,股票市場資金供應增加,股票價格將上升。

二是利率對上市公司經營的影響,進而影響公司未來的估值水平。

貸款利率提高會加重企業利息負擔,從而減少企業的盈利,進而減少企業的股票分紅派息,受利率的提高和股票分紅派息降低的雙重影響,股票價格必然會下降。相反,貸款利率下調將減輕企業利息負擔,降低企業生產經營成本,提高企業盈利能力,使企業可以增加股票的分紅派息。受利率的降低和股票分紅派息增加的雙重影響,股票價格將大幅上升。

三是利率變動對股票內在價值的影響。

股票資產的內在價值是由資產在未來時期中所接受的現金流決定的,股票的內在價值與一定風險下的貼現率呈反比關系,如果將銀行間拆借、銀行間債券與證券交易所的債券回購利率作為參考的貼現率,則貼現率的上揚必然導致股票內在價值的降低,從而也會使股票價格相應下降。股指的變化與市場的貼現率呈現反向變化,貼現率上升,股票的內在價值下降,股指將下降；反之,貼現率下降,股價指數上升。

以上的傳導途徑應該是較長的一個時期才能體現出來的,利率調整與股價變動之間通常有一個時滯效應,因為利率下調首先引起儲蓄分流,增加股市的資金供給,更多的資金追逐同樣多的股票,才能引起股價上漲,利率下調到股價上漲之間有一個過程。如我國央行自1996年5月以來的八次下調存款利率,到2002年1年期定期儲蓄存款的實際收益率只有1.58%。在股票價格在較長時間內持續上漲的情況下,股票投資的收益率遠遠高於存款的報酬率,一部分儲蓄存款轉化為股票投資,從而加快了儲蓄分流的步伐。從我國居民儲蓄存款增長率來看,1994年居民儲蓄存款增長率45.6%,之後增幅連年下滑,而同一時期股票市場發展迅速,1999年下半年開始儲蓄分流明顯加快,到2000年分流達到頂點,同年我國居民儲蓄存款增長率僅為7.9%。這一年股票市場也牛氣沖天。2001年儲蓄分流則明顯減緩,增長率14.7%,居民儲蓄傾向增強。2001年股市波動性加大,股價持續幾個月的大幅回調,則是2001年儲蓄分流減緩、居民儲蓄存款大幅增加的主要原因之一。

另外,利率對於企業的經營成本影響同樣需要一個生產和銷售的資本運轉過程,短時間內,難以體現出來。因此,利率和股票市場的相關性要從長期來把握。

實際上,就中長期而言,利率升降和股市的漲跌也並不是簡單的負相關關系。就是說,中長期股價指數的走勢不僅僅只受利率走勢的影響,它同時對經濟增長因素、非市場宏觀政策因素的反應也很敏感。如果經濟增長因素、非市場宏觀政策因素的影響大於利率對股市的影響,股價指數的走勢就會與利率的中長期走勢相背離。

典型如美國的利率調整和股市走勢就出現同步上漲的過程。1992年至1995年美元加息周期中,由於經濟處於穩步增長階段,逐步收緊的貨幣政策並未使經濟下滑,公司盈利與股價走勢也保持了良好態勢,加息之後,股票市場反而走高,其根本原因是經濟增長的影響大於加息的影響。

我國從1996年5月進入降息周期的拐點。股指也進入上升周期。利率與股指的走勢發生了5年的負相關關系。但2001年在利率沒有進入升息周期的情況下,股指開始了下跌的趨勢。分析其原因,我國非市場宏觀政策因素的影響大於利率對股市的影響。人們對非流通的國有股將進入市場流通的擔心和恐懼導致了股市投資的風險和收益發生了非對稱的變化。從這個角度來看,由於我國目前非市場宏觀政策因素仍然有比較大的不確定性,所以利率對股市的影響不能夠成為我們研究和預測股市中長期走勢的主要因素。

就短期而言,我國利率的變動對股價的走勢很難判斷存在相關性。利率調整當天和隨後的股價波動並不能說明二者之間有何必然的聯系。從當前股市的狀況分析,很明顯也和利率的走勢不符合理論上的負相關性。股票市場的低迷更多地被歸結為上市公司的質量以及諸多體制性問題和投資者信心問題。因此,在看待我國加息預期對於股票市場的影響時,還要考慮其他諸多因素,而不能簡單從前文所述的理論關系來判斷。利率只是影響股市的因素之一,而不是惟一決定因素。因此,我們不能唯利率升降是從,要具體分析,何況即使利率上升,股市也並不是就完全沒有投資機會。（

Interest rates. Most people pay attention to them, and they can impact the stock market. But why? In this article, we'll explain some of the indirect links between interest rates and the stock market and show you how they might affect your life.

The Interest Rate
Essentially, interest is nothing more than the cost someone pays for the use of someone else's money. Homeowners know this scenario quite intimately. They have to use a bank's money (through a mortgage) to purchase a home, and they have to pay the bank for the privilege. Credit card users also know this scenario quite well - they borrow money for the short term in order to buy something right away. But when it comes to the stock market and the impact of interest rates, the term usually refers to something other than the above examples - although we will see that they are affected as well. (To read more, see Who determines interest rates?)

The interest rate that applies to investors is the U.S. Federal Reserve's federal funds rate. This is the cost that banks are charged for borrowing money from Federal Reserve banks. Why is this number so important? It is the way the Federal Reserve (the "Fed") attempts to control inflation. Inflation is caused by too much money chasing too few goods (or too much demand for too little supply), which causes prices to increase. By influencing the amount of money available for purchasing goods, the Fed can control inflation. Other countries' central banks do the same thing for the same reason.

Basically, by increasing the federal funds rate, the Fed attempts to lower the supply of money by making it more expensive to obtain.(To see more on the Federal Reserve, read Get To Know The Major Central Banks, The Fed Model And Stock Valuation: What It Does And Does Not Tell Us and Formulating Monetary Policy.)

Effects of an Increase
When the Fed increases the federal funds rate, it does not have an immediate impact on the stock market. Instead, the increased federal funds rate has a single direct effect - it becomes more expensive for banks to borrow money from the Fed. However, increases in the discount rate also cause a ripple effect, and factors that influence both indivials and businesses are affected.

The first indirect effect of an increased federal funds rate is that banks increase the rates that they charge their customers to borrow money. Indivials are affected through increases to credit card and mortgage interest rates, especially if they carry a variable interest rate. This has the effect of decreasing the amount of money consumers can spend. After all, people still have to pay the bills, and when those bills become more expensive, households are left with less disposable income. This means that people will spend less discretionary money, which will affect businesses' top and bottom lines (that is, revenues and profits).

Therefore, businesses are also indirectly affected by an increase in the federal funds rate as a result of the actions of indivial consumers. But businesses are affected in a more direct way as well. They, too, borrow money from banks to run and expand their operations. When the banks make borrowing more expensive, companies might not borrow as much and will pay a higher rate of interest on their loans. Less business spending can slow down the growth of a company, resulting in decreases in profit. (For extra reading on company lending, read When Companies Borrow Money.)

Stock Price Effects
Clearly, changes in the federal funds rate affect the behavior of consumers and business, but the stock market is also affected. Remember that one method of valuing a company is to take the sum of all the expected future cash flows from that company discounted back to the present. To arrive at a stock's price, take the sum of the future discounted cash flow and divide it by the number of shares available. This price fluctuates as a result of the different expectations that people have about the company at different times. Because of those differences, they are willing to buy or sell shares at different prices.

If a company is seen as cutting back on its growth spending or is making less profit - either through higher debt expenses or less revenue from consumers - then the estimated amount of future cash flows will drop. All else being equal, this will lower the price of the company's stock. If enough companies experience a decline in their stock prices, the whole market, or the indexes (like the Dow Jones Instrial Average or the S&P 500) that many people equate with the market, will go down. (To learn more, check out Why Do Markets Move?, Forces That Move Stock Prices and What causes a significant move in the stock market?)

Investment Effects
For many investors, a declining market or stock price is not a desirable outcome. Investors wish to see their invested money increase in value. Such gains come from stock price appreciation, the payment of dividends - or both. With a lowered expectation in the growth and future cash flows of the company, investors will not get as much growth from stock price appreciation, making stock ownership less desirable.

Furthermore, investing in stocks can be viewed as too risky compared to other investments. When the Fed raises the federal funds rate, newly offered government securities, such Treasury bills and bonds, are often viewed as the safest investments and will usually experience a corresponding increase in interest rates. In other words, the "risk-free" rate of return goes up, making these investments more desirable. When people invest in stocks, they need to be compensated for taking on the additional risk involved in such an investment, or a premium above the risk-free rate. The desired return for investing in stocks is the sum of the risk-free rate and the risk premium. Of course, different people have different risk premiums, depending on their own tolerance for risk and the company they are buying. However, in general, as the risk-free rate goes up, the total return required for investing in stocks also increases. Therefore, if the required risk premium decreases while the potential return remains the same or becomes lower, investors might feel that stocks have become too risky, and will put their money elsewhere.

Interest Rates Affect but Don't Determine the Stock Market
The interest rate, commonly bandied about by the media, has a wide and varied impact upon the economy. When it is raised, the general effect is to lessen the amount of money in circulation, which works to keep inflation low. It also makes borrowing money more expensive, which affects how consumers and businesses spend their money; this increases expenses for companies, lowering earnings somewhat for those with debt to pay. Finally, it tends to make the stock market a slightly less attractive place to investment.

Keep in mind, however, that these factors and results are all interrelated. What we described above are very broad interactions, which can play out in innumerable ways. Interest rates are not the only determinant of stock prices and there are many considerations that go into stock prices and the general trend of the market - an increased interest rate is only one of them. Therefore, one can never say with confidence that an interest rate hike by the Fed will have an overall negative effect on stock prices.

❹ 關於股票投資策略的數學建模問題

風險最小就是相關系數之和最小的方案吧
投資回報率和風險的關系，就是收益期望和相關系數之間的函數
數學不好，只能亂說說了

❺ 股票投資數學建模問題

風險最小就是相關系數之和最小的方案吧
投資回報率和風險的關系，就是收益期望和相關系數之間的函數
數學不好，只能亂說說了

❻ 急求求一篇投資組合的收益與風險的數學建模論文

用一個項目的風險溢價（收益率減去無風險收益率 題目里銀行沒有損失的可能 所以無風險利率是5.5%）除以項目的標准差 得到了這個項目承擔一個標准差需要提升的收益率

通常這個數值越高 說明這個方案在同等風險下越有吸引力

可以根據風險損失率算出每個項目的標准差 然後用風險溢價除這個標准差

然後把錢投到各個項目上（由剛才的數值，從大到小投資）

【題目第一沒給出每個項目需要投資好多錢 二沒給出每個行業之間的協方差 這在里只能假設不同項目協方差為0】

❼ 數學建模股票問題

朋友多實戰學習吧！這才是股市成功的唯一道路，祝你好運！

❽ 股票問題 用MATLAB做數學建模

%文件vol.m
function f=vol(x);
A = [2.10 2.20 2.30 2.35 2.40];;
Ap = [200 400 500 600 100];

B = [2.00 2.10 2.20 2.30 2.40];
Bp = [800 600 300 300 100];

f = -min(sum(Ap(A <= x)), sum(Bp(B >= x)));
%------------------------------------------

>> [x fval] = fminsearch('vol',2.3)

x =

2.3000

fval =

-400

你說的低於和高於我理解成小於等於與大於等於了,不對的話在函數最後一行自己改

❾ 數學建模 找出一種有效的選股模式與投資策略

如果從時間著手股市的問題，那真是大錯特錯，徒勞無功。
時間每分每秒都在變化，即將發生的事全部是未知數。
股市中也許存在某些循環，但他們都與時間無關。證據就是與時間有關的指標都不是那麼准確，沒有任何一隻股票第一個10（n）天在波段的最低點而第二個10（n）天在波段的最高點。
建議：從價格趨勢price的k線形態著手，結合成交量vol、價值基本面value，找出至少四種形態漲、跌、平、盪。。。的選股模式與投資策略。這個需要自己動手，別人的方法也許並不適合你的實情。