Using mathematical ratios to evaluate the risk and returns of investment is a basic component of making investments.

You may have hated Maths especially the typical mathematical ratios in your school days, but now since you are on the path to becoming a value investors, you need to grip some numbers related to stocks or mutual funds that you intend to buy.

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Standard Deviation |

Beta Mathematical Ratios |

Sharpe Ratio |

Treynor Mathematical Ratios |

These terms or concepts are very vital to understand the inherent risk and return associated with investments.

These are Standard Deviation, Beta, Sharpe Ratio, and Treynor Ratio. Let us discuss all of them one by one.

**Standard Deviation**

Standard deviation simply quantifies how much a series of numbers, such as fund returns, varies around its mean, or average. Investors like using standard deviation because it provides a precise measure of how varied a fund’s returns have been over a particular time frame both on the upside and the downside.

With this information, you can judge the range of returns your fund is likely to generate in the future. The more a fund’s returns fluctuate from month to month, the greater it’s standard deviation.

For instance, a mutual fund that gained 1% each and every month over the past 36 months would have a standard deviation of zero, because its monthly returns didn’t change from one month to the next.

But here’s where it gets tricky: A mutual fund that lost 1% each and every month would also have a standard deviation of zero. Why? Because, again, its returns didn’t vary.

Meanwhile, a fund that gained 5% one month, 25% the next, and that lost 7% the next would have a much higher standard deviation; its returns have been more varied.

Standard deviation allows a fund’s performance swings to be captured into a single number. For most funds, future monthly returns will fall within one standard deviation of its average return 68% of the time and within two standard deviations 95% of the time.

**Beta Mathematical Ratios**

A beta is a statistical tool, which gives you an idea of how a fund will move in relation to the market. In other words, it is a statistical measure that shows how sensitive a fund is to market moves

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Let us consider 3 possible scenarios in interpreting beta numbers:

[Sensex is assumed as benchmark index].

1. A beta of 1.0 indicates that the fund Net asset value (NAV) will move in the same direction as that of the benchmark index. The fund will move up and down in tandem with the movement of the markets (as indicated by the benchmark)

2. A beta of less than 1.0 indicates that the fund NAV will be less volatile than the benchmark index.

3. A beta of more than 1.0 indicates that the investment will be more volatile than the benchmark index. It is an aggressive fund that will move up more than the benchmark, but the fall will also be steeper.

For example, if the beta of “ABC-Equity (G)” is 1.4 – then it’s considered as 40% more volatile than the benchmark index (beta of benchmark index being 1).

Similarly, in example-1, as we have considered beta of “ABC-Equity (G)” fund as 0.69 – this means the mutual fund scheme will be less volatile than its benchmark index.

Conservative investors should focus on mutual funds schemes with low beta. Aggressive investors can opt to invest in mutual fund schemes which have higher beta value for higher returns taking more risk.

**Sharpe Ratio**

The Sharpe ratio uses standard deviation to measure a fund’s risk-adjusted returns. The higher a fund’s Sharpe ratio, the better a fund’s returns have been relative to the risk it has taken on. Because it uses standard deviation, the Sharpe ratio can be used to compare risk-adjusted returns across all fund categories.

Developed by its namesake, Nobel Laureate William Sharpe, this measure quantifies a fund’s return in excess of our proxy for a risk-free, guaranteed investment (the 90-day Treasury bill) relative to its standard deviation.

To calculate a fund’s Sharpe ratio, first, subtract the return of the 90-day Treasury bill from the fund’s returns, then divide that figure by the fund’s standard deviation. If a fund produced a return of 25% with a standard deviation of 10 and the T-bill returned 5%, the fund’s Sharpe ratio would be 2.0: (25-5)/10.

The higher a fund’s Sharpe ratio, the better its returns have been relative to the amount of investment risk it has taken. For example, both State Street Global Research SSGRX and Morgan Stanley Inst. European Real Estate MSUAX has enjoyed heady three-year returns of 23.9% through August 2004. But Morgan Stanley sports a Sharpe ratio of 1.09 versus State Street’s 0.74, indicating that Morgan Stanley took on less risk to achieve the same return.

The higher a fund’s standard deviation, the higher the fund’s returns need to be to earn a high Sharpe ratio. Conversely, funds with lower standard deviations can sport a higher Sharpe ratio if they have consistently decent returns.

Keep in mind that even though a higher Sharpe ratio indicates a better historical risk-adjusted performance, this doesn’t necessarily translate to a lower-volatility fund. A higher Sharpe ratio just means that the fund’s risk/return relationship is more proportional or optimal.

**Treynor Mathematical Ratios**

Treynor mathematical ratios shows the risk-adjusted performance of the fund. Here the denominator is the beta of the portfolio. Thus, it takes into account the systematic risk of the portfolio.

Jack Treynor extended the work of William Sharpe by formulating Treynor ratio. Treynor ratio is similar to Sharpe ratio, but the only difference between the ratios is that of the denominator.

The formula for Treynor ratio: (Rp-Rf)/Beta

where,

Rp: Return on the portfolio

Rf: Risk-free rate

B: Beta, the sensitivity of the portfolio to changes in the overall market.

Unlike Sharpe, Treynor uses beta in the denominator instead of the standard deviation. The beta measures only the portfolio’s sensitivity to the market movement, while the standard deviation is a measure of the total market volatility both upside as well as the downside. A fund with a higher Treynor ratio implies that the fund has a better risk-adjusted return than that of another fund with a lower Treynor ratio.

More than calculation, these ratios are important from the point of interpretation and what they say about a security.

You may have hated math in your school days, but now that you are on the path to becoming a valuable investor, you need to grip some numbers related to stocks or mutual funds that you intend to buy. These terms or concepts are very vital to understand the inherent risk and return associated with investments. To learn more about the basics of stock market, you can download Elearnmarkets learning app.

Hope these numbers will help in making informed decisions.

Happy Reading!!