Mathematics plays a crucial role in share dealing and investing, providing tools for analyzing stock performance, evaluating risks, and making informed decisions. Here’s how you can use math effectively in share dealing:

Understanding Key Financial Metrics

Price-to-Earnings (P/E) Ratio

• Formula: P/E Ratio=Market Price per ShareEarnings per Share (EPS)\text{P/E Ratio} = \frac{\text{Market Price per Share}}{\text{Earnings per Share (EPS)}}P/E Ratio=Earnings per Share (EPS)Market Price per Share​
• Purpose: Compares a company’s current share price to its earnings, helping assess if a stock is overvalued or undervalued.

Dividend Yield

• Formula: Dividend Yield (%)=Annual Dividends per SharePrice per Share×100\text{Dividend Yield (\%)} = \frac{\text{Annual Dividends per Share}}{\text{Price per Share}} \times 100Dividend Yield (%)=Price per ShareAnnual Dividends per Share​×100
• Purpose: Indicates the return on investment from dividends relative to the stock price.

Earnings Per Share (EPS)

• Formula: EPS=Net Income−Preferred DividendsAverage Outstanding Shares\text{EPS} = \frac{\text{Net Income} – \text{Preferred Dividends}}{\text{Average Outstanding Shares}}EPS=Average Outstanding SharesNet Income−Preferred Dividends​
• Purpose: Measures profitability on a per-share basis.

2. Portfolio Diversification and Risk Management

Expected Return of a Portfolio

• Formula: $$\text{Expected Return (ER)}=\sum \left(\text{Weight of Stock}\times \text{Expected Return of Stock}\right)$$
• Purpose: Helps predict the potential return of a diversified portfolio.

Portfolio Variance and Standard Deviation

• Variance Formula: σp2=∑(wi2×σi2)+∑∑(2×wi×wj×Cov(i,j))\sigma^2_p = \sum \left( w_i^2 \times \sigma_i^2 \right) + \sum \sum \left( 2 \times w_i \times w_j \times \text{Cov}(i,j) \right)σp2​=∑(wi2​×σi2​)+∑∑(2×wi​×wj​×Cov(i,j)) Where $w$ is the weight, σ2\sigma^2σ2 is the variance of each stock, and $\text{Cov}(i,j)$ is the covariance between stocks.
• Purpose: Measures the risk (volatility) of the portfolio. Lower variance indicates less risk.

Beta Coefficient

• Formula: β=Covariance of Stock and MarketVariance of Market Returns\beta = \frac{\text{Covariance of Stock and Market}}{\text{Variance of Market Returns}}β=Variance of Market ReturnsCovariance of Stock and Market​
• Purpose: Indicates a stock’s sensitivity to market movements. A beta greater than 1 implies higher volatility than the market.

3. Compound Interest and Growth

Future Value of Investment

• Formula: FV=PV×(1+r)tFV = PV \times (1 + r)^tFV=PV×(1+r)t Where $PV$ is the present value, $r$ is the annual growth rate, and $t$ is the number of years.
• Purpose: Predicts how investments grow over time, incorporating reinvested returns.

Continuous Compounding

• Formula: FV=PV×ertFV = PV \times e^{rt}FV=PV×ert Where $e$ is the mathematical constant (~2.718).
• Purpose: Provides a more accurate growth calculation for frequently compounded investments.

4. Technical Analysis

Moving Averages

• Simple Moving Average (SMA): SMA=Sum of Prices over n DaysnSMA = \frac{\text{Sum of Prices over n Days}}{n}SMA=nSum of Prices over n Days​
• Purpose: Smooth out price data to identify trends over time.

Relative Strength Index (RSI)

• Formula: RSI=100−1001+Average GainAverage LossRSI = 100 – \frac{100}{1 + \frac{\text{Average Gain}}{\text{Average Loss}}}RSI=100−1+Average LossAverage Gain​100​
• Purpose: Measures the speed and change of price movements to identify overbought or oversold conditions.

Standard Deviation in Volatility

• Formula: σ=∑(xi−xˉ)2n−1\sigma = \sqrt{\frac{\sum (x_i – \bar{x})^2}{n-1}}σ=n−1∑(xi​−xˉ)2​

Spectacular performances are not confined to growth stocks. Another group worth watching is recovery shares. Most companies at some time or times in their careers strike a difficult patch, which may be the result of mismanagement, changes in fashion, excessive competition, a general slump, losses on raw materials or stocks, or some other factor. Some companies go to the wall in such circumstances. Others struggle along as shadows of their former glorious selves.

And some – as a result of the turn of the trade cycle, reorganization, a change of control, or the infusion of new enterprise or products – recover fairly quickly, or after an uphill grind. A good example is the Rank Organization which after being successively hit by heavy losses on film production, and a big decline in cinema-going, boldly met its problems by reorganization and expansion into electronics, light engineering, and other forms of entertainment such as bowling alleys.

In appreciation of the recovery taking place and the future potential of the greatly diversified interests, the 5s. ordinary shares came out of the Stock Exchange ‘dog-house’ to become a long-term popular investment at some seven to eight times the price to which they had dropped when few financial experts had a good word for them.

Whatever the Mathematical formula  or basic plan adopted, it is a good idea to take into account of the following investment rules:

1. Spread the risk, particularly in equity shares, so that if one company or industry strikes a bad patch it does not affect the whole portfolio.

2. Be ready to switch. Never look at a portfolio as static. Even if it means selling at a loss, it is a sound policy to switch from an investment which is declining or static to one which is dynamic, and always be willing to Learn how to trade in new and innovative ways as this always helps.

Check out some incredible Math Lessons below:

 

Gold shares demonstrate the effect of factors over which individual companies and entire industries have no control. The gold-mining industry, unlike other industries, has thus been hamstrung in its efforts to meet big rises in production costs. Although it now costs much more to dig an ounce of gold out of the ground, the dollar price is the same as in 1939.

Faith in gold shares has, in consequence, dwindled, until they are brushed aside as a waste of time or treated solely as gambling counters. Yet (political factors in the producing countries apart) any change of American policy resulting in a more realistic selling price would bring a big change in sentiment; gold-mining shares might then retrieve some of their lost glamour.
Price movements in the stock market as a whole, or among individual sections or currently popular stocks, are not always one way.

Framing the right investment policy in present conditions is not easy. The first major point to decide is whether the emphasis must be put on (a) immediate income or (b) capital growth. Retired people, or those nearing retirement, may have little choice but to opt for income. Younger investors, who are not dependent on income from savings, may however prefer to spread their holdings in ways which could add to the capital value and so enlarge their self-generated pension fund. Sometimes we need to be reminded that trading in stocks and shares is very similar to Mathematical Roulette, in that it is a gamble.

Other important points to take into account are the amount to be invested, or saved and the risks which can or should be taken – all equities do not improve in value over the years; a quite high proportion lose ground.

Despite the attractions of a 100 per cent equity investment program it may therefore pay to follow the older policy of having part of one’s funds in fixed-interest stocks. The proportion will depend on individual needs, circumstances, and the amount of capital. Whereas, in Mathematical terms, for instance, 10-25 per cent might be enough where the emphasis is on growth, 50 per cent or more might be essential for those heavily dependent on investment income, it is wise to review Share prices. It is interesting to note in this respect that the investment experts who advise the successful clients of one big football pool favour a fifty-fifty policy. We are also discussed on the Nemeth Braille Code resource page here.