Applications of mathematics and statistics in financial markets

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Presentation transcript:

Applications of mathematics and statistics in financial markets Mohammed Al-Grenees 8th February 2017

Percentage gains and losses I purchase 10 stocks of stock A worth $100 each. Stock price declines 50% in Day 1 … increases by 50% in day 2 Did I generate zero profits? Did I gain money or lose money?

Percentage gains and losses Actually I lost money! When the stock price declined by 50%, it went from $100 to $50. In Day 2 when it increased by 50%, it increased by only $25 to $75. Hence, overall I lost 25% even though the stock fell by 50% and then subsequently increased by 50%. This is important lesson. Do not be confused!

Measuring stock returns I bought stock A in 31.Dec.2011, then: Year 2012: 90% Year 2013: 10% Year 2014: 20% Year 2015: 30% Year 2016: -90% Average: 12%

Measuring stock returns Because of 2016 decline, the investor lost 67% of his capital, losing SAR 673,960

What is a trend line? A trend line is a line of best fit that represents a behavior of a data set over a time period to determine if there is a particular pattern. For example, is the price line upward sloping or downward sloping?

Saudi Stock Market Index

TASI Monthly Returns The standard deviation is 0.25 (or 25%)

SABIC Monthly Price Performance Beta of 1.02

SABIC Monthly Returns The standard deviation is 0.36 (or 36%)

Rajhi Monthly Price Performance Beta of 0.91

Rajhi Monthly Returns The standard deviation is 0.34 (or 34%)

Coca-Cola Monthly Price Performance Beta of 0.75

Coca-Cola Monthly Return The standard deviation is 0.17 (or 17%)

Oil Monthly Price Performance

Oil Monthly Returns The standard deviation is 0.32 (or 32%)

US Treasuries (20yr)

US Treasuries Monthly Returns The standard deviation is 0.13 (or 13%)

US Treasuries Yield 10-Years

Regression Analysis Y=bX+a Y is the dependent variable (sales) X is the independent variable (GDP) Correlation Spurious Correlation Beta

Oil and Saudi GDP 1969-1980 Correlation of 0.89

Oil and Saudi GDP 1981-1997 Correlation of 0.61

Oil and Saudi GDP 1998-2015 Correlation of 0.88

M1 Vs TASI

Historical Valuation P/E (SAUDI)

Historical Valuation P/B (SAUDI)

Historical Valuation P/E (US)