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### If investors are risk-neutral, should the (equity) risk premium be zero?

I looked up ChatGPT and they stated that the (equity) risk premium should be zero for a risk-neutral world. The definition of a risk-neutral investor is that one is indifferent between additional or ...
61 views

### Estimating risk premium with cross sectional regression

I am trying to estimate a carbon risk premium according to the Fama & MacBeth methodology using a cross-sectional regression approach. Therefore, I regress the excess return in period t+1 on the ...
191 views

### How are the risk premiums (SMB, HML) calculated for the Fama-French factor model

The question is assuming a Fama-French model, how should we calculate the expected return of an asset? To do this according to arbitrage pricing theory requires the risk premiums of the 3 factors, but ...
1 vote
58 views

### 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 ...
78 views

### 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 ...
42 views

### 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 ...
581 views

### 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 $\lambda$ ...
1 vote
75 views

### 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 ...
136 views

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 ...
79 views

### 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 ...
1 vote
127 views

461 views

### 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 ...
987 views

### 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: ...
3k views

### What is time-varying risk premium? Forecasting stock returns

I am trying to understand the concept 'Time-varying aggregate risk premium'. Here is an extract from a Forecasting book, written by Rapach and Zhou, "However, rational asset pricing theory posits ...
86 views

### 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 ...
117 views

### 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 ...
1 vote
165 views

### 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 ...
249 views

### 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 ...
542 views

### 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 ...
1 vote
107 views

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 $V(S(t), t) = e^{rt}\... 3 votes 3 answers 2k views ### Is forward price trendless under the real-world measure? I recently went through some commodities forward curve modeling documentations, where a diffusion model for the forward price$F(t,T)$was modeled as a driftless diffusion process (as a function of t ... 1 vote 0 answers 489 views ### 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 ... 1 vote 1 answer 446 views ### 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 ... 0 votes 0 answers 95 views ### 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 ... 5 votes 0 answers 308 views ### 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 ... 2 votes 3 answers 2k views ### 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 ... 3 votes 2 answers 711 views ### 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 ... 13 votes 1 answer 529 views ### 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 ... 9 votes 4 answers 1k views ### 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 ... 12 votes 1 answer 607 views ### 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$- Present Value of cash ... 16 votes 12 answers 167k views ### How to calculate unsystematic risk? We know that there are 2 types of risk which are systematic and unsystematic risk. Systematic risk can be estimate through the calculation of β in CAPM formula. But how can we estimate the ... 7 votes 3 answers 780 views ### Debunking risk premium via "hedging" argument? (or why even in the real world$\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 ...