Questions tagged [standard-deviation]

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17 views

What kind of standard deviation? [closed]

Can someone help me convert the following standard deviation into something I can actually use e.g. in Excel? Also I don't understand why the T-1 is taken to the power of 0.5? The problem at the ...
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23 views

Labeling Returns in 5 categories based on BL view approach

I have to label a time series of returns into 5 categories based on the Black Litterman view approach. The categories should look as follows: very bullish: + 2 std. dev. bullish: + 1 std. dev. ...
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41 views

Dorfleitner's Standard Deviation

Can someone please advise how to compute the following (as my results go into thousands): E.g. I have used and the result (for T=12) = 580103.7261 Thanks
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37 views
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1answer
106 views

In-sample volatility measurement

I would like to know what is the most reasonable way to measure volatility in a sample of past observations. Aside from standard deviation, are more complex models like GARCH used for (historical) ...
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1answer
49 views

Efficient Frontier Graph

I'm writing some C code to create different portfolios using a few stocks that are given as inputs. I am having some trouble trying to find if these results are correct. My biggest hesitation is that ...
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1answer
60 views

Annualising standard deviation (monthly, quarterly data)

The question I have refers to annualised standard deviation. For example, I have various funds monthly returns data for the period 1980-2019. Some of them report data for e.g. 13, 19, 43, 56 months ...
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2answers
50 views

Annualisation of Downside Deviation

Is it possible to annualise the downside deviation? If so, on the basis of what theory? The downside deviation (DD) of a series of daily returns is computed according to the formula: $\text{DD} = \...
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23 views

Disalignment between global standard deviation and mean of rolling standard deviation

Ciao, I am working on proprerties of time series. I was trying to deduce an estimate of standard deviation of a process from the series of rolling standard deviation but I've got some issues when I ...
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1answer
77 views

Markowitz expected return time

This is perhaps a rather silly question for the more experienced people in the community but it has been puzzling my mind for a while. Let's say we have a portfolio of 10.000 dollar. We will apply ...
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1answer
151 views

Interpretation of IV and its use in stock movement prediction

I would like to validate my understanding of IV as a prediction tool. Black-Scholes model is based on the assumption that rate of return of a stock is a Wiener process: $$ \frac{dS_t}{S_t} =\mu \,...
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151 views

Overlapping Data

I have a daily time series data spanning over 22 years. I need to compute some meaningful yearly standard deviation statistics / generate probability distribution and estimate tail risk. 22 years ...
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1answer
582 views

How to have an unbiased estimation of the standard deviation when using rolling returns?

I want to estimate the weekly standard deviation of a lognormal process in a usual setup. $$ \frac{dS}{S} = (\dots) dt + \sigma dW $$ where $\sigma$ is a constant and $W$ a brownian motion. The ...
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1answer
600 views

Calculate Idiosyncratic Risk?

I have basic finance background but I am trying to calculate idiosyncratic risk as measure for firm risk in my CEO gender research. I have found the following on Alpha architect but I am unsure of ...
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1answer
65 views

Can you clarify Kelly's derivation in Paul Wilmott Introduces Quantitative Finance?

Can anybody explain how the $\phi_i$ became $\mu$ and how $\phi_i^2$ became $\sigma^2$. Am I correct to assume that since $\phi_i$ is the outcome, $\mu$ is the average of the outcome? But I don't ...
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2answers
162 views

Standard deviation of a long-short portfolio with net position zero

I've come across the following question and I'm slightly stuck in answering it: Suppose you have a two-stock portfolio that is long one stock of asset A, and short one stock of asset B, with A ...
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1answer
222 views

Log returns: volatility, outperformance, Sharpe/information ratios

I have developed the habit of simply stating that a 21% return compared to a 10% benchmark return means that the outperformance was 10% (not 11%). So, treating the whole thing in a multiplicative way, ...
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1answer
75 views

Calculate standard deviation from the value at risk

I have the following data: VaR VaR% Expected return Am I right to think that I would be able to derive standard deviation from this? Using the formula: VaR%= ER-(zscore*SD), I should be able to ...
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1answer
402 views

What is the formulat to compute Tracking Error?

I am here for the first time and read quite a few posts before asking this question. In my class, my finance Professor wrote the formula for Tracking Error $TE$: $$TE = \sqrt{(1-R^2)} \times \sigma$$ ...
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97 views

Units of Risk: Variance vs Standard Deviation

Suppose you are trading two mean-reverting assets, A and B, and that $Covar(A, B) > 0$. You are currently long one unit of A, and are considering buying one unit of B. Compared to the situation ...
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1answer
203 views

A portfolio with two risky assets - Simple exercise

I was trying to solve the following exercise: "Stocks A have $\mu_A=8\%$, $\sigma_A=2,5\%$ and stocks B have $\mu_B=6\%$, $\sigma_B=1,2\%$. Let us suppose that expexted returns are independent. What ...
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226 views

How do the units compare inside the (rate - 0.5*sigma-squared) correction?

Usually, I find the units of the mean and the standard deviation of a distribution to be (quite obviously) the same. Can anyone come up with a really simple explanation (for MBA students, some of ...
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1answer
67 views

How can certain numerical distributions yield misleading standard deviation calculations? [closed]

What numerical distributions yield misleading standard deviation calculations? Can you make the standard deviation of distribution 1 attain a higher value than the standard deviation of distribution ...
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2answers
240 views

Correlation between two indexes

The Global Minimum Variance has an annual return standard deviation of 9.9%. Its correlation with the Standard & Poor's 500 Index is 0.45. What is the annual return standard deviation of the S&...
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3answers
424 views

Mean and standard deviation of price series with Kalman

I like to calculate the mean and standard deviation of a price series, using the Kalman filter. I am somehow stuck with the deviation, or have some problem in understanding, which my research could ...
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1answer
4k views

Why do two perfectly negatively correlated assets not return 0%? [closed]

So, per the title, why would a combination of two risky assets that have the same exact expected return and standard deviation while being perfectly negatively correlated not return 0%? Why do you ...
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1answer
279 views

How do I find the standard deviation of a portfolio? [closed]

Compute the expected return $\mu_V$ and standard deviation $\sigma_V$ of a portfolio consisting of three securities with weights $\omega_1=40\%$, $\omega_2=-20\%$, $\omega_3=80\%$, given that the ...
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1answer
36 views

Compute the risk measured by the standard deviations $\sigma K_1, \sigma K_2, \sigma K_3$, does this have to do with weights?

Compute the risk measured by the standard deviations $\sigma K_1, \sigma K_2, \sigma K_3$ for each of the investment projects, where the returns $K_1, K_2$, and $K_3$ depend on the market scenario: $$...
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3answers
914 views

Appropriate measure of risk if return are not normally distributed

Normally standard deviation of an assets is used as an proxy for the risk in the financial market. In reality distribution of return is more peaked at the center and higher mass in the tail as ...
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1answer
66 views

Volatility of monthly performances, where the last month is short

I'd like to calculate the vol of a return series of, say, 25 months. However, the last of those months is not completed yet. The last data point only refers to the first 21 days of the month (say, ...
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2answers
504 views

Estimation of annualized volatility depending on data frequency - exceptions to the general rule?

From my understanding, the annualized standard deviation of daily returns is generally higher than of annualized standard deviation of weekly returns is generally higher than.... monthly...quarterly......
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2answers
142 views

Problem with obtaining densities

For my research I need to obtain a series of densities, however, I am encountering some problems. The first problem is perhaps very simple, but the answer eludes me. Let's say I have an observation ...
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3answers
895 views

Sharpe Ratio : why the normalization factor?

I try to understand why a $\sqrt{252}$ normalization factor is useful for Sharpe Ratio: Let's compute the Sharpe Ratio for this imaginary portfolio, for various sampling periods: ...
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1answer
62 views

How to calculate 5 years return & STD for ETF?

I want to calculate by-myself 5 year return & STD for SPY ETF. What I did: Downloaded to Excel from yahoo finance historical data for the ETF (daily Adj. Close) from ...
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1answer
395 views

Impulse response function interpretation

I would need a quick help with Impulse response function interpretation which I have done after Vector autoregression model in stata. I need to understand how to interpret IRF graph or table values ...
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4answers
2k views

Calculating portfolio risk

I want to calculate the risk of a portfolio with the following. In order to calculate the following formula: However, I am not sure if I have to use log returns or simple returns to calculate the ...
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2answers
1k views

Annualized Sharpe Ratio calculation

I'm trying to replicate the annualized Sharpe ratio of an buy-and-hold strategy for the Dow Jones Industrial Average index for a period consisting of multiple years. I got the daily DJIA (closing) ...
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1answer
68 views

Isolating single assets standard deviation in a portfolio accounting for correlation

I am running a simple Monte Carlo analysis in Excel using mean return, standard deviation and the =NORMINV(RAND(),mean,std dev) method. I have a correlation matrix that I use to compute the portfolio ...
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1answer
838 views

Multiplying by the Square Root of Twelve to calculate annual standard deviation

I failed to see the mathematics truism. Can someone care to elaborate.
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3answers
915 views

Is implied volatility flawed?

Was going through how Implied Volatility is used by option traders and in delta hedging. Correct me if I am wrong, doesn't IV consider a standard deviation of the stock price over say the past 1 year? ...
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2answers
96 views

Does anyone know where I can find a free efficient frontier tool, or an informative and legitamate/academic graph of the efficient frontier?

I'd like to build a portfolio based upon modern portfolio theory and I'd like to find a tool I can use to calculate the proper mix of asset classes. Can anyone help with this? I think a good chart/...
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1answer
220 views

Computing the minimum variance portfolio

Given two risky assets and their corresponding covariance matrix, how do I compute the global minimum variance portfolio, its standard deviation and its expected return?
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6answers
25k views

Relationship between Beta and Standard Deviation

I was doing some financial analysis on two firms in the coffee industry. After calculating Beta and Standard Deviation for both firms, I seem to have stumbled on some weird phenomenon. It appears ...
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1answer
263 views

Is the market really Normal. Is Implied Volatility Historically Correct?

Ok. So as of 6/10/2014's market close the SPY was 195.6 and the VIX closed at a ridiculous recent low of 10.99. Now because the VIX (IV) is the implied volatility of 1 month contracts on the SPX and ...
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2answers
168 views

Standard Deviation as listed in Rebonato's Volatility and Correlation: Binomial Replication 2.3.4 Worked-Out Example

I am reading Rebonato's Volatility and Correlation (2nd Edition) and I think it's a great book. I'm having difficulty trying to derive a formula he used that he described as the expression for ...
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2answers
9k views

Sharpe Ratio, annualized monthly returns vs annual returns vs annual rolling returns?

I would like to calculate the Yearly Sharpe Ratio on MSCI World index I have monthly values of the index that falls back up to Jan/1970, hence about: 44 years, 528 months In order to calculate ...
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1k views

Formula for the efficient portfolios (mean-variance optimisation)?

Consider the setting of mean-variance portfolio optimisation: $n$ assets with expected returns $\overline{r}_1,...,\overline{r}_n$ and standard deviations $\sigma_1,...\sigma_n$. For a certain fixed $...
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2answers
7k views

Why do stocks with a negative beta return less than the risk free rate?

Let's say we have two stocks, Stock A and Stock B. Both of them have the same standard deviation $\sigma$, and therefore have the same risk. The only difference is that Stock A has a perfect ...
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4answers
2k views

compute sharpe ratio for options?

Calculating sharpe ratio for shares is a straight forward task: (average returns - risk free ) / standard deviation. However i remain baffled as to how to tackle the task for options, can someone ...