Estimating a Stock’s Closing-Price Probability from Beta and Specific Volatility

Summary

The document poses a one-day probability question using a stock’s beta, stock-specific daily volatility, its previous closing price, and the market’s move during the day. It asks for the probability that the stock closes at or above a stated threshold after the market rises. This setup points toward separating the stock’s market-linked return from its idiosyncratic component, then estimating the chance that the residual move is large enough to reach the target price.

No solution or assumptions are supplied. In particular, the question does not state a distribution for the stock-specific return, clarify whether volatility is a standard deviation under a normal model, or describe how beta and the market move map to the stock’s return over the day. Those modeling choices affect the resulting probability, so the provided inputs alone do not yield a unique answer. The document is a short quantitative exercise prompt rather than an explanation of an estimation method or evidence from market data.

Key ideas

• The question relates a stock’s beta and specific daily volatility to a one-day closing-price probability.
• Beta links the stock’s return to the market move, while specific volatility represents stock-level variation.
• The requested event is whether the ending price meets or exceeds a stated threshold.
• A probability calculation requires assumptions about the distribution of the specific return.
• The document provides no worked solution or empirical evidence.

Tags

# Stock Price Question


# Stock Price Question












Can anyone show me how to answer this please?

A stock has beta of 2.0 and stock specific daily volatility of 0.04. Suppose that yesterday’s closing price was 95 and today the market goes up by 3%. What’s the probability of today’s closing price being at least 98?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.