Questions tagged [risk-premium]

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Betas and weighted average ERP

Whenever analyzing a particular company through CAPM, I used to take the Equity Risk Premium (ERP) of the country where the company was listed/headquartered. However, recently I came to know that some ...
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Risk premium of insurance risk

I recently came across an equation in a paper. In short, suppose that $I(t)$ denotes a longevity index at time $t$. An informative indicator that is useful in the absence of any information about the ...
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Premium density under stochastic interest rate

First, suppose that the interest rate is assumed to be zero. Then, according to the definition provided by Delbaen and Haezendonck (1989), the premium is given by: \begin{equation} p_t = p(\mathbb{Q})\...
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Pricing of factors - portfolio sorts

if I read that someone is using portfolio sorts to determine whether a factor is priced in the cross section ( risk premium ) is it the two-pass Fama-MacBeth regression? Is there a material that would ...
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How to determine the risk premium from the Vasicek one factor model?

The short rate under the Vasicek one factor model under the real-world measure $\mathbb{P} $ follows : $$ dr(t)=(a\theta - (a+\lambda \sigma)r(t))dt + \sigma dW(t),$$ $$ r(0)=r_0 $$ where $ \lambda $ ...
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Measuring extra return investors demand for a stock which cannot be sold?

How to roughly measure how much premium investors would demand if a stock could not be sold and its investors had to stick with it permanently using just dividends not capital gain as return? I am not ...
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ETF NAV Premium vs. market ETF premium interpretation regression output

this is my first post in this forum, so if I'm doing any kind of mistake please let me know. My situation is as follows: I'm currently writing my Thesis and I'm looking into the discrepancies of ETF ...
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Electricity Futures Risk Premiums With ARIMA

I am attempting to model long-term electricity prices using today's futures prices. Unlike most futures, electricity is delivered over a period of time (usually a month), rather than at a point in ...
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1 answer
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Market price of risk of different maturities

T. Bjork Arbitrage Theory in Continuous Time Proposition 23.1 "Assume that the bond market is free of arbitrage. Then there exists a process $\lambda$ such that the relation $\frac{\alpha_T(t)-r(...
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2 votes
1 answer
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Low volatility in factor regression

Let's say we are working with the standard Fama-French 3 factor model and we want to add a low volatility factor. Is it alright to add a low volatility risk premium in a model such as the CAPM or FF3. ...
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3 answers
535 views

Why exposure to the profitability factor increases investment premium?

I'm a DIY investor that attempts to put together his market portfolio, tilted to increase factor exposure. Currently, I'm trying to do it based on the French-Fama 5-factor model. This model contains ...
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2 answers
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How is the risk premium of the index estimated?

In the construction of an index model, we often use the expected return of a security, including surprises, for analysis. To calculate this, we must estimate the risk premium of the index. Since we ...
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What is risk premium of a portfolio?

I am not an expert in the field. So bear with me if my terminology is bad. I want to understand what risk premium of a portfolio is. I understand that there are different forms of risk. The basic ...
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3 votes
1 answer
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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 ...
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Value premium analysis - Equal or Value-weighted Portfolios?

I got a question regarding the analysis of the value premium in the U.S. stock market. The task is to use the market-to-book-value ratio to split the S&P500 in five portfolios (rank 1-100,101-200,...
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Is there a robust way to calculate stock beta or factor exposure that's specific to crashes?

Commonly known factors like market, value, momentum etc. have positive expected returns because they draw-down unexpectedly and investors require a risk premium for holding them. This idea is extended ...
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Estimation of market price of risk of short interest rate under the Hull-White model

I think I am a bit confused. I intend to estimate the market price of risk the short interest rate, say, under the Hull-White model. I have the following two questions. Is it correct to state state ...
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Estimation of the variance risk premium via VIX

Suppose I have the formula for computing $\mathbb E^P\big[\int_0^T v\,dt\big]$ for the variance process $v$ in the real world measure $P$. Can I set it to the VIX$^2$ price and solve for the variance ...
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The positivity of the market price of risk

Does the market price of risk, be it of stochastic volatility, interest rate or equity return, have to be positive? What is the rationale if it does?
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Forward looking estimation of market price of risk of stochastic volatility

I would like to estimate the market price of stochastic volatility by forward looking methods, such as option values. The stochastic volatility model I have in mind is the Heston model or some other ...
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1 vote
4 answers
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If equity returns are normally distributed, why are average equity returns not zero [closed]

So I am getting confused between assumption of equity returns normality and why then equity markets in the long term on average go up i.e equity risk premium. Does this not already poke wholes in the ...
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4 votes
4 answers
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Intuitively, why does liquidity premium contribute to bond yield?

According to the Wikipedia, "The upwards-curving component of the interest yield can be explained by the liquidity premium... Liquidity risk premiums are recommended to be used with longer term ...
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1 answer
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Correct choice of SMB factor for regression models

I am currently conducting a performance analysis, where I use the 3-, 4-, and 5-factor models, hence $R_{it}-R_{Ft}=\alpha+b_{i}RMRF+s_{i}SMB+h_{i}HML$ $R_{it}-R_{Ft}=\alpha+b_{i}RMRF+s_{i}SMB+h_{i}...
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Behavioral SDF: modelling sentiment risk premium

With reference to Behavioral Asset Pricing models, I know that the discount factor (or required rate of return) is equal to: Discount rate = Risk-free rate + Fundamental risk premium + Sentiment ...
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3 votes
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Derivation of the Pnl of a Delta Hedged Straddle and Risk Reversal

In the link below, in the text it states the following equations: Delta-hedged straddle P&L = Volatility Risk-premium ×| Straddle Vega | and Delta-hedged risk-reversal P&L: ...
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Heuristic (or algorithm) for calculating a risk premium, given a probability of default and a "minimum" profit margin (expressed as a yield)

Assuming that I have means of determining and calculating the following metrics: Risk (i.e. probability*) of a default to a particular borrower as P Profit margin of X% The profit margin is taken to ...
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5 votes
0 answers
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Why use sovereign default risk to determine equity risk premiums?

Damodaran's paper "Equity Risk Premiums..." (2016) discusses the standard of using various measures of sovereign default risk (e.g. Moody's ratings, bond default spreads, CDS spreads) to estimate ...
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Short-rate models: Risk-premium of $T$-bonds

Following "Arbitrage Theory in Continuous Time" by Thomas Bjork, a standard one-factor short-rate model is of the form \begin{align*} dr_t = \mu(t,r_t)dt + \sigma(t,r_t)dW_t. \end{align*} The only ...
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Definition of factor premium: against cap weighted index or against treasury bills?

How can we define a factor premium? In the book Berkin & Swedroe: Your Complete Guide to Factor-Based Investing the authors start introducing the market bet premium and define it as the average ...
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3 votes
1 answer
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Basis swap pricing dynamics

The existence of basis spreads leads to that e.g. a 6M forward rate has a different price than two after each other following 3M forward rates. This due to that the 6M forward rate has a higher credit ...
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1 answer
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Is it possible to approach finding the risk premium of this derivative using Ito's Lemma?

I understand the author's intended solution to the below problem, but I thought I would see if I could solve this using first principles and Ito's Lemma instead for practice. Let $V(S(t), t) = e^{rt}\...
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3 votes
3 answers
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Is forward price trendless under the real-world measure?

I recently went through some commodities forward curve modeling documentations, where a diffusion model for the forward price $F(t,T)$ was modeled as a driftless diffusion process (as a function of t ...
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1 vote
0 answers
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Cross-sectional Regression: Using calculated coefficient of first regression for a second regression as dependent variable

Hello stackexchange community! I am new to R and econometrics and and stuck in a step of the fama-macbeth (1973) regression, in which risk premia of stocks are estimated with a two-step regression ...
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1 answer
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PPPN: participation rate, stocks and premium

I'm a student of financial engineering and am very new to all of this stuff. Now, I'm trying to make an "example of a beginners exercise", but alas, I don't have any clue on how to solve or even on ...
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Input for unanticipated risk premium estimation

In the paper "Economic Forces and the Stock Market" by Chen, Roll and Ross, unanticipated risk premium (URP) is tested as a potential risk factor for stock returns. This factor is commonly calculated ...
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ERP and FF 3-factor model

In a more conservative estimate than a simple historical average, Fama & French estimate (US) equity risk premium at 3-4% (e.g., Equity Risk Premium, JF, 2002). This suggests that in an APT-like ...
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3 answers
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What is the clean price and dirty price of a risky bond?

Following up on this question: Yield of a risky bond, what is the definition of clean and dirty prices for a risky (defaultable, catastrophe, etc.) bond? I would think the dirty price should ...
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3 votes
2 answers
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When gains are made: Overnight or during trading hours? What is the connection to volatility?

Falkenblog reports an interesting finding: All of the stock returns since 1993 are from overnight returns and cross-sectionally, volatility receives a positive overnight risk premium, a negative ...
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13 votes
1 answer
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Is Arithmetic Return Bias Basis of Low Vol Anomaly?

An observation in capital markets is that the connection between return and risk (measured as volatility) is not that straightforward (at least not as modern portfolio theory assumes). One interesting ...
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8 votes
4 answers
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Why should there be an equity risk premium?

After years of mathematical finance I am still not satisfied with the idea of a risk premium in the case of stocks. I agree that (often) there is a premium for long dated bonds, illiquid bonds or ...
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12 votes
1 answer
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Creating an n-factor Certainty Equivalent Discounting Formula

Brealey & Myers provide a certainty-equivalent version of the present value rule, using CAPM, as follows: $$PV_0=\frac{C_1 - \lambda_m *cov(C_1, r_m)}{1 + r_f}$$ $PV_0$ - Present Value of cash ...
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17 votes
12 answers
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How to calculate unsystematic risk?

We know that there are 2 types of risk which are systematic and unsystematic risk. Systematic risk can be estimate through the calculation of β in CAPM formula. But how can we estimate the ...
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7 votes
3 answers
749 views

Debunking risk premium via "hedging" argument? (or why even in the real world $\mu$ should equal $r$)

Since I began thinking about portfolio optimization and option pricing, I've struggled to get an intuition for the risk premium, i.e. that investors are only willing to buy risky instruments when they ...
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18 votes
7 answers
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Are there ways to measure the risk aversion of a representative investor, based on publicly available market data?

Are there ways to measure the risk aversion of a representative investor, based on publicly available market data? Public available data could include asset price, volume, and flow data, and may be ...
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