Questions tagged [variance]

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11answers
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Lévy alpha-stable distribution and modelling of stock prices.

Since Mandelbrot, Fama and others have performed seminal work on the topic, it has been suspected that stock price fluctuations can be more appropriately modeled using Lévy alpha-stable distrbutions ...
8answers
51k views

What is the difference between volatility and variance?

How do volatility and variance differ in finance and what do both imply about the movement of an underlying?
5answers
19k views

Why would an investor trade a variance swap over a volatility swap?

Why would an investor trade a variance swap over a volatility swap? Is it simply related to the leverage involved in a Var (i.e. sigma-squared) or is there something else to it?
4answers
935 views

Approximately what proportion of a stock’s volatility is explained by market movement?

Assume we decompose the daily (log) returns of a stock as beta times market movement plus an idiosyncratic part. If this is done ex-ante, what proportion of the variance is explained by the market ...
2answers
390 views

3answers
780 views

CAPM model as a regression

The CAPM model states that the returns of a stock are- $r_s=r_f+\beta (r_m-r_f)+\varepsilon_s$ The $\beta$ defined above is then calculated as $\frac{cov(r_s,r_m)}{var(r_m)}$. My question is ...
3answers
2k views

Variance swap replication and variance vega

Noob here. I've been trying to gain a better understanding of variance swaps and what better way than to replicate it with a portfolio of better understood instruments. I have read the GS 1999 ...
2answers
735 views

What are the significant implications of the long-run average variance rate and why Engle won the Nobel Prize for ARCH model development?

In a ARCH(m) model we have $$\sigma_n^2=\sum_{i=1}^{m} \alpha_i u_{n-i}^2$$ where $u_i$ is defined as the continuously compounded return during day $i$ (between the end of day $i-1$ and the end of ...
2answers
545 views

Choice of prior as a shrinkage target in portfolio construction?

There's various research showing how priors such as the minimum variance portfolio turn out to be a surprisingly effective shrinkage target in portfolio construction. The sell point of these priors ...
1answer
211 views

How to scale option pricing components in regard to time

I am looking at closed-form options approximations, in particular the Bjerksund-Stensland model. I have run into a very basic question. How should I scale the input variables in regard to time? My ...
2answers
288 views

1answer
148 views

Risk, required return and expected volatility - what is the relationship?

Return required from risk averse agents from risky investments are proportional to expected return variance. That is from the textbook, you take the portfolio with the highest return to standard ...
3answers
439 views

Negative variance?

Using the formula w*Cov*t(w) I can generate a negative portfolio variance. What are the implications of a negative variance? Should I just assume it's zero? A negative variance is troublesome ...
1answer
3k views

Using CAPM to find correlation of two assets with each other

I stumpled upon an exercise in an investments book: The data below describe a three-stock financial market that satisfies the single-index model. ...
2answers
2k views

GARCH variance vs standard deviation for volatility

in my series of questions related to GARCH and volatility I finally think I've got a decent grasp on it. You guys have been great help clearing up my questions for me. My next question is just a ...