Questions tagged [risk-premium]
The risk-premium tag has no usage guidance.
40
questions
3
votes
2answers
234 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
1answer
73 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 ...
0
votes
1answer
68 views
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 ...
2
votes
0answers
58 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
1answer
106 views
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(...
2
votes
1answer
87 views
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. ...
3
votes
3answers
405 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 ...
0
votes
2answers
81 views
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 ...
0
votes
1answer
88 views
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 ...
3
votes
1answer
83 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 ...
1
vote
1answer
98 views
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,...
0
votes
1answer
118 views
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 ...
0
votes
1answer
793 views
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 ...
1
vote
0answers
150 views
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 ...
5
votes
1answer
308 views
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?
2
votes
0answers
63 views
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 ...
1
vote
4answers
762 views
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 ...
4
votes
4answers
317 views
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 ...
1
vote
1answer
167 views
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}...
5
votes
1answer
396 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 ...
3
votes
0answers
684 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:
...
0
votes
1answer
60 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 ...
5
votes
0answers
104 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
1answer
140 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 ...
4
votes
1answer
219 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 ...
3
votes
1answer
488 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
1answer
92 views
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}\...
3
votes
3answers
1k 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
0answers
417 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
1answer
300 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
0answers
91 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 ...
4
votes
0answers
259 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
3answers
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
2answers
698 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
1answer
505 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 ...
8
votes
4answers
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
1answer
595 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 ...
17
votes
12answers
157k 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
3answers
740 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 ...
18
votes
7answers
2k views
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 ...
