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Questions tagged [risk-premium]

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1answer
27 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,...
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1answer
42 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 ...
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0answers
47 views

Calculating WACC for Google, What should be Market Risk premium

I am at beginner level in Finance. I want to calculate WACC for the Google I am considering risk free rate from treasury reports 30 years data. Not sure about market risk premium. Please guide.
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1answer
372 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 ...
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0answers
123 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 ...
4
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1answer
101 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?
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0answers
41 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
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4answers
342 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 ...
3
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4answers
173 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
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1answer
117 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
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1answer
251 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 ...
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0answers
333 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: ...
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1answer
45 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
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0answers
92 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
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1answer
99 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
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1answer
160 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
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1answer
420 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
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1answer
78 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
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3answers
510 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 ...
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0answers
292 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
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1answer
204 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 ...
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0answers
84 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 ...
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0answers
238 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 ...
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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 ...
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2answers
623 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
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1answer
485 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 ...
7
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4answers
990 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
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1answer
564 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 ...
13
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12answers
127k 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
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3answers
669 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
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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 ...