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31 votes
5 answers
7k views

What methods do you use to improve expected return estimates when constructing a portfolio in a mean-variance framework?

One of the main problems when trying to apply mean-variance portfolio optimization in practice is its high input sensitivity. As can be seen in (Chopra, 1993) using historical values to estimate ...
Karol J. Piczak's user avatar
22 votes
3 answers
2k views

How are distributions for tail risk measures estimated in practice?

Let's say you want to calculate a VaR for a portfolio of 1000 stocks. You're really only interested in the left tail, so do you use the whole set of returns to estimate mean, variance, skew, and shape ...
Richard Herron's user avatar
17 votes
9 answers
10k views

Why the expected return rate of a stock has nothing to do with its option price?

OK, I admit that this is a frequently asked question. But I couldn't find a satisfying answer after I read the explanations of books, went through the derivations of B-S formula, and searched answers ...
Allanqunzi's user avatar
17 votes
2 answers
9k views

How does left tail risk differ from right tail risk?

How does left tail risk differ from right tail risk? In what context would an analyst use these metrics?
user389's user avatar
  • 171
13 votes
1 answer
1k views

Portfolios from Sorts

Some time ago Almgren and Chriss proposed a method for portfolio optimization based on sorting criteria such as $r_1 > r_2 >... > r_N$ instead of explicit expected returns: see portfolios ...
Felix's user avatar
  • 906
12 votes
3 answers
2k views

What is the expected return I should use for the momentum strategy in MV optimization framework?

As all research on the momentum strategies are focused on the indicator, i.e. the entry point, there seems not much discussion on its expected return? Though there are some discussions on the exit ...
Jason's user avatar
  • 123
10 votes
1 answer
5k views

How to apply the Kelly criterion when expected return may be negative?

My concern is how to handle a negative value for the Kelly formula. Even when you have a system that has positive expectancy, you can (and usually will) sustain a number of losses, sometimes ...
Brian's user avatar
  • 101
10 votes
1 answer
2k views

Expected return from a multiple linear regression?

How can I compute the predicted return from a linear regression that includes a number of different terms. For instance, suppose my equation is: $r_{future} = \alpha + \beta_1 r_{history} + \beta_2 ...
Belmont's user avatar
  • 401
9 votes
2 answers
235 views

St Petersburg lottery pricing & short investing horizons

I am a statistician (no solid background in finance). Please forward me to a book \ chapter \ paper to resolve the following general question. Suppose we have a stock with the following monthly return ...
Tim's user avatar
  • 131
8 votes
2 answers
2k views

How does return-based analysis calculate expected return of a trading system?

Suppose you have a trading system that is never flat, but either long or short the market. You have four years of performance. During that period, your system changed its position 10 times. So you ...
Milktrader's user avatar
7 votes
2 answers
710 views

Intuitive explanation of stochastic portfolio theory

Fernholz and Karatzas have published various papers about so called stochastic portfolio theory. Basically they say that the return to be expected from a portfolio on the long run is rather the ...
Richi Wa's user avatar
  • 13.7k
7 votes
3 answers
247 views

Where to find good notations to teach investment portfolio maths?

I don't know whether this question is in order here. I do a bit of teaching and I am preparing my own notes but I thought that his should not be necessary. In which book/pdf on the web can we find a ...
Richi Wa's user avatar
  • 13.7k
7 votes
2 answers
281 views

Do all risky assets have negative expected return over long enough time horizons?

I stumbled across a site that claims "given a long enough forecast horizon H, all assets with positive volatility have an unbiased expected return that is negative". They base this on the ...
Kalev Maricq's user avatar
6 votes
1 answer
293 views

How to perform cross-sectional asset pricing regression?

I'm wondering is that possible to get insignificant beta estimates in the time-series context, but highly significant risk premium associated with that beta in the cross-sectional regression? Any ...
SNU's user avatar
  • 135
6 votes
2 answers
3k views

What are the assumptions in the first-stage of Fama-MacBeth (1973)?

According to the CAPM, the expected return of asset $i$ is: $E(Z_i) = \beta_{im} E(Z_m)$ where $Z_m$ is the excess return on the market portfolio, and $Z_i$ is the excess return of asset $i$ over ...
user27808's user avatar
4 votes
1 answer
263 views

Methods for superior estimates of returns in m.v. portfolio optimization

Leaving aside the aspects related to the estimation of the variance component (all the latest techniques to compute a stable covariance matrix of a given set of assets such as simple shrinkage, Ledoit-...
Nipper's user avatar
  • 359
4 votes
1 answer
464 views

Delta derivation from the expectation

I'm trying to understand the following transformation leading to Delta $\frac{dC}{dx} = e^{-r\tau} \mathbb{E}[ \frac{\partial}{\partial x}\text{max}(xY-K,0)] = e^{-r\tau} \mathbb{E}[Y \textbf{1}(xY&...
rollerboller's user avatar
4 votes
1 answer
319 views

Measuring expected returns

Most papers in the literature measure expected returns using the simple average of past returns. Why is this? When is it more correct to use geometric returns instead? Any good references? I know that ...
phdstudent's user avatar
  • 8,381
4 votes
1 answer
123 views

What should happen to the equity risk premium as rates change?

Suppose I set forward-looking expected returns for capital markets using a dividend discount model framework, under which expected return for equities is the sum of dividend yield, expected trend ...
beeba's user avatar
  • 1,074
4 votes
0 answers
96 views

How is option pricing related to the correlation between implied volatlity and the underlying?

The correlation between the index returns (e.g SPX) and its changes in option-impled volatility (e.g. VIX), is strong, stable and negative (the implied volatility feedback effect). To me at least, it ...
Mats Lind's user avatar
  • 1,412
3 votes
1 answer
522 views

Expected return on Black-Scholes priced option?

Suppose we have a European-style call option on some stock, and it was priced according to Black-Scholes. Everybody agrees on the stock's volatility and expected return. What's the expected return (...
Axel Boldt's user avatar
3 votes
1 answer
155 views

How to calculate the expected stock returns for an individual stock?

I know about CAPM. My question is if this method is also viable: Calculate monthly logReturns ...
A. Henderson's user avatar
3 votes
3 answers
2k views

How to model the daily return using intraday data?

Say, I have hourly returns $r_1,r_2,...,r_T$, where $r_t$ = $ln(p_t)$ - $ln(p_0)$ for $t = 1...T$. So what is the value of $E[r_t]$? Would $r_T$ be the $\prod{(r_t)}$? Basically $r_t$s are the ...
Antelope's user avatar
3 votes
1 answer
645 views

Call option on a Mutual Fund

I am trying to price a call option on a mutual fund. Given the lack of market implied data, I am going to estimate the fund´s expected volatility using as a reference its historical volatility (...
sets's user avatar
  • 1,471
3 votes
1 answer
2k views

How to estimate market integration parameter in Singer-Terhaar model for E(r)?

Singer-Terhaar is part of CFA II and III curriculum. It estimates risk premium for some asset, traded at some local market, as weighted average of expected premiums for the case of (1) local market, ...
Alexander Didenko's user avatar
3 votes
1 answer
267 views

Trading a Bouncy Stock

I came across the following question and am trying to understand it better. I was hoping you could share your intuitions. For a given stock, you are certain that for the next 100 days, it will move ...
FoxCharles's user avatar
3 votes
1 answer
364 views

Mean-variance maximization

I denote by $W_0$ and $W_1$ the wealth of an investor at $t=0$ and $t=1$, respectively. Let $r_f$ be the risk free rate, $r$ the vector of returns of the risky assets in excess of the risk free rate, ...
Dadoo's user avatar
  • 39
3 votes
0 answers
48 views

Polynomial interpolation of corrected lognormal distribution

Can anyone provide a formula for a polynomial interpolation of the corrected lognormal distribution used to model returns traditionally resulting from the wrong Brownian motion generated model? ...
Jack Maddington's user avatar
3 votes
0 answers
51 views

Characterizing relation " has no less information than" between information systems represented by Markovian matrices

I crossposted this question on math.stackexchange. Background: Suppose that an investor's utility is both determined by the state and her action taken. A fact of life is that she can't observe the ...
Bender's user avatar
  • 73
3 votes
0 answers
399 views

Correlation between idiosyncratic residuals and forward returns

The classic mean-reversion strategy is to calculate an "expected return" (alpha) by computing the raw return for each security and then remove the part which you think is market driven. Statistically ...
statquant's user avatar
  • 1,288
2 votes
2 answers
446 views

Why are long 2 year Treasury futures (ZT) trading at negative carry?

The 2 year Treasury note yields ~4.9% in the cash market as of 29 Aug 2023. Assume implied cost of financing of 5.5% pa (3 month T-bill rate) to finance a long futures position. This results in a ...
craftcase's user avatar
2 votes
1 answer
149 views

How can risk-neutral pricing find the right price for securities if it doesn't account for risk premia?

I'm confused as to how a method that values securities purely on their expected return works in the real world if it doesn't take into account the fact that investors demand a higher return for ...
Vinegar Strauss's user avatar
2 votes
1 answer
2k views

Computing the minimum variance portfolio for only two risky assets

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?
user2034's user avatar
  • 215
2 votes
1 answer
265 views

Expected option return in MATLAB

The expected return of an option is given by its expected payoff under $P$ over its market price under $Q$. For the Black-Scholes model, expected call option return is given as (see here): $$ E(R)=\...
emcor's user avatar
  • 5,795
2 votes
1 answer
220 views

Trying to understand the notion of required return

I have been thinking about the notion of required return lately. I am not familiar with a formal definition, but I have tried to reason my way towards one. Please let me know if my approach makes ...
Richard Hardy's user avatar
2 votes
1 answer
107 views

relation between risk averson coefficient and maximum Sharp ratio in Black-Litterman context

BL model compute the implied returns based on the reverse optimization where the objective is: $${\underbrace U_{{\rm{investor's \ risk \ utility}}} \buildrel \Delta \over = {\bf{w}}_M^T{\bf{\Pi }} - \...
sci9's user avatar
  • 123
2 votes
1 answer
74 views

Why do surprises in macroeconomic variables average out to zero?

In the book Investments (Bodie, Kane, Marcus), in chapter 8, the authors discuss index models (page 247) and, in its context, systematic risk. The authors state, without explanation, that the market ...
Aditya Verma's user avatar
2 votes
2 answers
301 views

2 stocks, no shorting vs shorting. (concrete questions, mean-variance)

I'd appreciate help with the following questions. Suppose there are two stocks $A$ and $B$ with expected returns $E_A, E_B >0$ and volatilities $v_A, v_B >0$, respectively . Also, suppose ...
user9482's user avatar
2 votes
1 answer
878 views

T-statistics on monthly returns vs annualized monthly returns

eqI am very confused about a very basic question. This is probably more statistics than quantitative finance, but still, should be useful for this stackexchange board as well. Let's assume I have ...
phdstudent's user avatar
  • 8,381
2 votes
1 answer
519 views

Understanding CAPM, CML, and efficient portfolios

I'm trying to understand the CAPM model and how we can use it to understand efficient portfolios. Specfically, I'm trying to use the CML line (mapping expected returns and standard deviations of ...
standarddev's user avatar
2 votes
1 answer
37 views

Distress firms and cross section returns

In George and Hwang's 2010 JFE paper, they are trying to resolve the so called distress risk and leverage puzzles. This is their explanation: This is a puzzle because high distress intensity or ...
zsljulius's user avatar
  • 660
2 votes
0 answers
115 views

Does the expected return increase with variance for stocks? [duplicate]

I took a historical dataset of ~2600 stocks and computed the 30-day returns for non-overlapping windows, for a 9 year period. For the returns, I computed the mean and variance. Then I plotted the mean ...
Botond's user avatar
  • 121
2 votes
0 answers
93 views

Expected returns and Fama-French Factor Model

It is my understanding that for any given stock, the sample mean of historical returns is not a good proxy for the stock's expected return. In fact, the return on a stock needs to be estimated via ...
John Paris's user avatar
2 votes
0 answers
126 views

A Bayesian-Stein based expected return estimator by J.P. Morgan

Please consider the following estimator for the expected returns specified in the paper "Improving on risk parity: Hedging forecast uncertainty" by Peter Rappoport, J.P. Morgan, October 2012....
Nipper's user avatar
  • 359
2 votes
0 answers
99 views

Are there any studies on the link between energy markets and hedging-strategies for Cryptocurrency mining?

Full Disclaimer: I first asked this question on Bitcoin.SE, however I feel like my question is more relevant to this site as there would be wider knowledge and insight of some better sources or ...
Hamish Gibson's user avatar
2 votes
1 answer
917 views

Under Put-Call Parity, why do we add the cost of carry to Call prices but subtract them from the Stock price and Put prices?

In Natenberg (1994) Chapter 11 he outlines the Put-Call parity relationships. ...
user avatar
2 votes
0 answers
57 views

Inferring Returns From Minimal Data Points [duplicate]

Possible Duplicate: How much data is needed to validate a short-horizon trading strategy? Suppose I have daily returns for a trading strategy against one month of data. Before starting trading on ...
Aziz's user avatar
  • 121
2 votes
1 answer
115 views

Is it possible to calculate the equity required (or expected) return using Black-Scholes option pricing model?

I know the method of calculating the equity value as a European call option (using Black-scholes formula). My question is: Is it possible to calculate the expected (or required) return of equity when ...
Saeed Fathi's user avatar
1 vote
2 answers
246 views

Are asset return means difficult to predict because they have no lower bound?

In finance, it is widely known that the volatility of asset returns ($\sigma$) are easier to predict than the expected value of asset returns ($\mu$) , otherwise known as the average return or mean. ...
develarist's user avatar
  • 3,000
1 vote
2 answers
497 views

Intuitive explanation of geometric mean

Suppose that the 10 Year Treasury Yield Rate varies every trading day during the year X1 (which in practice is accurate) what is the intuitive explanation behind calculating the geometric mean using ...
Dmitriy's user avatar
  • 75