The Discounted Cash Flow (DCF) model allows to obtain the fair value of a stock as the present value of the expected cash flows the company will generate in the future. The thesis aims to provide an approximation of the model in continuous time, arising from the arguments that we are considering an infinite time horizon in which the terminal years account for the most of the present value. Thus, we aim to provide either a closed-form solution or an approximation in continuous time (exploiting integrals), reducing the number of parameters to be estimated in cash flows' formulas and the accounting assumptions generally needed in financials' estimation. We call the specification Continuous DCF Model, and provide various formulations depending on different functions that model future expected growth in time; particularly, we study the case of Stable Growth function, Two-Stages growth and the known H-Model. The dataset covers roughly eight years of data, up to May 2022; it refers to nine American listed stocks, chosen to resemble the idea of Super Stocks, as defined by American investment analyst Kenneth Fisher in his book in 1984. Generally, we intend Super Stocks as stocks experiencing a tremendous growth in time, which could further be obtained or maintained stable; we recognized in the Super Stocks' concept the relevance of the bound between growth and time, and since it is also crucial for the functions studied in the thesis we chose to analyse such sample of stocks. The results of the analysis show how every model employed produces estimates of the intrinsic value of the examined stock coherent with the actual valuations observed in the market. Moreover, we have been able to compare the different specifications of the model and to drive conclusions about their precision and flexibility in usage: the Two-Stage model can be easily computed by hand, is strongly grounded on financial theory and able to provide sensible results. The H-Model specifications result to be more involved and complex, but are likely to be more precise. Finally, we conclude the thesis by presenting theoretical applications of the continuous DCF approach to the equity duration concept.
Il modello Discounted Cash Flow (DCF) consente di ottenere il valore intrinseco di un titolo come valore attuale dei flussi di cassa attesi che l'azienda genererà in futuro. La tesi si propone di fornire un'approssimazione del modello DCF nel tempo continuo, dato che il modello considera un orizzonte temporale infinito in cui i periodi più lontani nel tempo contribuiscono per la maggior parte del valore attuale finale. Pertanto, la tesi mira a fornire una soluzione in forma chiusa o un'approssimazione in tempo continuo (sfruttando quindi gli integrali), riducendo il numero di parametri da stimare nelle formule dei flussi di cassa e le ipotesi contabili generalmente necessarie nella stima dei fondamentali finanziari. Chiamiamo la specificazione ottenuta “DCF Continuo” e forniamo varie formulazioni a seconda delle diverse funzioni che modellano la crescita futura prevista nel tempo; in particolare, studiamo il caso della funzione di Crescita Stabile, della Crescita a Due Stadi e del noto H-Model. Il dataset utilizzato considera circa otto anni di dati, fino a maggio 2022; si riferisce a nove titoli americani quotati, scelti in riferimento all'idea di Super Stocks, come definito dall'analista di investimenti americano Kenneth Fisher nel suo libro del 1984. In generale, intendiamo le Super Stocks come titoli che abbiano sperimentato un'elevata crescita nel tempo, che potrebbe ancora essere raggiunta o mantenuta stabile; abbiamo individuato nel concetto di Super Stock l’importanza del legame tra crescita e tempo, e poiché tale relazione è cruciale anche per le funzioni studiate nella tesi abbiamo scelto di utilizzare tale campione di titoli. I risultati dell'analisi mostrano come ogni modello impiegato produca stime del valore intrinseco del titolo in esame coerenti con le effettive valutazioni osservate sul mercato. Inoltre, siamo stati in grado di confrontare le diverse specificazioni del modello e di trarre conclusioni sulla loro precisione e flessibilità nell'uso: il modello di Crescita a Due Stadi può essere facilmente calcolato manualmente, è fortemente fondato sulla teoria finanziaria e in grado di fornire risultati sensati. Le formulazioni dell’H-Model risultano essere più complesse e laboriose, ma possono essere ritenute più precise. Infine, concludiamo la tesi presentando le applicazioni teoriche dell'approccio del DCF Continuo al concetto di equity duration.
Valutazione Avanzata: il caso delle Super Stocks nel tempo continuo
BENINI, SIMONE
2021/2022
Abstract
The Discounted Cash Flow (DCF) model allows to obtain the fair value of a stock as the present value of the expected cash flows the company will generate in the future. The thesis aims to provide an approximation of the model in continuous time, arising from the arguments that we are considering an infinite time horizon in which the terminal years account for the most of the present value. Thus, we aim to provide either a closed-form solution or an approximation in continuous time (exploiting integrals), reducing the number of parameters to be estimated in cash flows' formulas and the accounting assumptions generally needed in financials' estimation. We call the specification Continuous DCF Model, and provide various formulations depending on different functions that model future expected growth in time; particularly, we study the case of Stable Growth function, Two-Stages growth and the known H-Model. The dataset covers roughly eight years of data, up to May 2022; it refers to nine American listed stocks, chosen to resemble the idea of Super Stocks, as defined by American investment analyst Kenneth Fisher in his book in 1984. Generally, we intend Super Stocks as stocks experiencing a tremendous growth in time, which could further be obtained or maintained stable; we recognized in the Super Stocks' concept the relevance of the bound between growth and time, and since it is also crucial for the functions studied in the thesis we chose to analyse such sample of stocks. The results of the analysis show how every model employed produces estimates of the intrinsic value of the examined stock coherent with the actual valuations observed in the market. Moreover, we have been able to compare the different specifications of the model and to drive conclusions about their precision and flexibility in usage: the Two-Stage model can be easily computed by hand, is strongly grounded on financial theory and able to provide sensible results. The H-Model specifications result to be more involved and complex, but are likely to be more precise. Finally, we conclude the thesis by presenting theoretical applications of the continuous DCF approach to the equity duration concept.È consentito all'utente scaricare e condividere i documenti disponibili a testo pieno in UNITESI UNIPV nel rispetto della licenza Creative Commons del tipo CC BY NC ND.
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https://hdl.handle.net/20.500.14239/2693