<blockquote>
<p>Do negative-cashflow properties imply greater appreciation?</p>
</blockquote>
<p>More or less yes, it depends on what creates the negative cash flow. Generally speaking the long run relationship between rents and house prices can be expressed as follows;</p>
<p><span class="math-container">$$R_t = P_t[(i_t + τ p_t )(1 − τ y_t ) + δ_t + λ_t − E_tG_{t+1}], \tag{*}$$</span></p>
<p>where <span class="math-container">$i_t$</span> is the real interest rate, <span class="math-container">$τ p_t$</span> is the property tax rate, <span class="math-container">$τ y_t$</span> is the marginal
income tax rate, <span class="math-container">$δ_t$</span> is the combined maintenance and depreciation rate, <span class="math-container">$λ_t$</span> is the  risk premium associated with housing, and <span class="math-container">$E_tG_{t+1}$</span> is expected capital gains (<a href="https://www.federalreserve.gov/pubs/feds/2004/200450/200450pap.pdf" rel="nofollow noreferrer">Gallin 2004</a>).</p>
<p>The cashflow that someone who owns and rents a house would get would be in essence;</p>
<p><span class="math-container">$$R_t - P_t[(i_t + τ p_t )(1 − τ y_t ) - m_t] =CF(P)$$</span></p>
<p>where <span class="math-container">$m_t$</span> is portion of <span class="math-container">$\delta$</span> spent on maintenance (<span class="math-container">$d_t$</span> is portion that is depreciation). Next the we can rearrange * and solve for capital gains to get;</p>
<p><span class="math-container">$$-\frac{R_t - P_t[(i_t + τ p_t )(1 − τ y_t ) - m_t] }{P_t} -d_t - \lambda =  E_tG_{t+1}, \tag{**}$$</span></p>
<p>Or;</p>
<p><span class="math-container">$$-\frac{CF(P_t) }{P_t} -d_t - \lambda =  E_tG_{t+1}$$</span></p>
<p>The equation above shows, that if the cashflow is higher then the expected capital gains from the houses are lower. However, there is a caveat. The cash flow depends negatively on <span class="math-container">$P$</span> but <span class="math-container">$P$</span> is both in numerator and denominator. Hence, if the negative cash flow is due to fall in rents, increase in interest rate, taxes or maintenance yes, if due to increase in the house price the effect depends on whether the change in numerator dominates the change in denominator.</p>
<blockquote>
<p>Can it be implied by the efficient market hypothesis (EMH) and the fact that these properties otherwise yield a relatively low ROI that this higher rate of appreciation will likely continue?</p>
</blockquote>
<p>I do not see how that is implied by EMH. First, efficient market hypothesis is typically a hypothesis that is applied to stock markets. Theoretically you could apply it to other asset prices I suppose but to my best knowledge it is not applied to housing market.  However, suppose we were to apply it housing market.</p>
<p>Efficient market hypothesis just says that asset prices are unpredictable because all avaiable information is already 'priced in' the price of asset. That is not the same as saying the price of asset does not depend on some fundamentals. It just means that all knowledge about the fundamentals is already reflected in the price so any price change is due to some new unexpected information. Inasmuch I can't see how this would violate EMH if applied to house prices. EMH doesn't claim there won't be trend in the aggregate prices. It just claims the individual prices will follow random walk around a trend given by fundamentals.</p>
<p>Also, your question makes it seems like Cambridge house prices always increase by 0.5% faster, but your own data show that is clearly not the case. Your own data you linked show that the prices in Cambridge sometimes increase faster sometimes slower than in rest of the England. In fact I am not even sure where yo got the 0.5% figure. The <a href="https://www.ons.gov.uk/visualisations/housingpriceslocal/E07000008/" rel="nofollow noreferrer">site</a> you used as a source does not mention that.</p>
<blockquote>
<p>He also states that he's almost 100% sure that the housing market would drop, which also seems to violate the EMH.</p>
</blockquote>
<p>Again not sure how this would violate EMH. I am almost 100% sure stock market will be increasing on average over next 50 years. Neither Sal's or mine obesrvation violates EMH. EMH says the price of individual asset is unpredictable, it doesn't say you cannot predict long term trends on stock market etc. You just can't do better than market on average.</p>

CC BY-SA 4.0
2024-08-17T12:28:11.663Z
The EMH implies than consistent alpha generation is impossible. There are indirect ways you could short the housing market if you knew it was going down to achieve alpha, no? Or without making a formal arbitrage argument: If there is not an appreciation premium, then these housing markets have negative alpha, so why would firms invest in them?
Zaz
CC BY-SA 4.0
2024-08-17T12:36:51.840Z
@Zaz yes because alpha is measure for active investments, not passive tracking of the market. EMH does not say it’s not possible to earn return by investing into stock market. It just says you cannot earn more than normal return.
1muflon1
CC BY-SA 4.0
2024-08-15T22:13:39.413Z
2024-08-15T22:13:39.413Z
1muflon1
<p>Some areas, such as the Bay Area in California and Cambridge, England have housing that, not accounting for appreciation, have a poor ROI compared to housing in the rest of the country due to <a href="https://www.sofi.com/learn/content/price-to-rent-ratio-in-50-cities/" rel="nofollow noreferrer">comparatively very low rental income</a>.</p>
<p>Properties in Cambridge, for example, have appreciated 0.5% faster, on average, than properties in the rest of Great Britain over the past 20 years, based on my analysis of <a href="https://www.ons.gov.uk/visualisations/housingpriceslocal/E07000008/" rel="nofollow noreferrer">ONS data</a>. Comparing appreciation in Cambridge to Great Britain, there is a standard deviation of 7.5% vs 5.9% and a 71% correlation between the two. Can it be implied by the efficient market hypothesis (EMH) and the fact that these properties otherwise yield a relatively low ROI that this higher rate of appreciation in valuable beyond what would be predicted by the CAPM and will likely continue?</p>
<p>If not, how could it be that houses are overpriced? Is it possible that bias of locals towards owning their own house affects the housing prices? If so, why doesn't this drive investors away, thereby increasing rents?</p>
<p>In <a href="https://www.khanacademy.org/economics-finance-domain/core-finance/housing/renting-v-buying/v/renting-vs-buying-a-home" rel="nofollow noreferrer">a Khan Academy video</a>, Sal looks at the example of a typical Bay-area home and concludes that appreciation should not be considered and that renting is a better choice than buying. He also states that he's almost 100% sure that the housing market would drop, which also seems to violate the EMH. Is it not the case that the house is expected to appreciate a significant amount, and hence the poor ROI in other aspects? If not, why does the typical Bay-area house violate the EMH?</p>

CC BY-SA 4.0
2024-08-15T21:29:49.200Z
If you feel this question needs more details, please offer suggestions how I could clarify it further.
Zaz
<microeconomics><investment><housing><efficient-markets>
Do negative-cashflow properties imply greater appreciation?
Zaz
# Do negative-cashflow properties imply greater appreciation?

(Asked by: username_0 on 2024-08-15)

Some areas, such as the Bay Area in California and Cambridge, England have housing that, not accounting for appreciation, have a poor ROI compared to housing in the rest of the country due to [comparatively very low rental income](https://www.sofi.com/learn/content/price-to-rent-ratio-in-50-cities/).

Properties in Cambridge, for example, have appreciated 0.5% faster, on average, than properties in the rest of Great Britain over the past 20 years, based on my analysis of [ONS data](https://www.ons.gov.uk/visualisations/housingpriceslocal/E07000008/). Comparing appreciation in Cambridge to Great Britain, there is a standard deviation of 7.5% vs 5.9% and a 71% correlation between the two. Can it be implied by the efficient market hypothesis (EMH) and the fact that these properties otherwise yield a relatively low ROI that this higher rate of appreciation in valuable beyond what would be predicted by the CAPM and will likely continue?

If not, how could it be that houses are overpriced? Is it possible that bias of locals towards owning their own house affects the housing prices? If so, why doesn't this drive investors away, thereby increasing rents?

In [a Khan Academy video](https://www.khanacademy.org/economics-finance-domain/core-finance/housing/renting-v-buying/v/renting-vs-buying-a-home), Sal looks at the example of a typical Bay-area home and concludes that appreciation should not be considered and that renting is a better choice than buying. He also states that he's almost 100% sure that the housing market would drop, which also seems to violate the EMH. Is it not the case that the house is expected to appreciate a significant amount, and hence the poor ROI in other aspects? If not, why does the typical Bay-area house violate the EMH?

**Tags:** microeconomics, investment, housing, efficient-markets

> **Comments:**
> **username_0**: If you feel this question needs more details, please offer suggestions how I could clarify it further.  

---

## 1 answers

### Answer by username_1 on 2024-08-15. Score: 1

> Do negative-cashflow properties imply greater appreciation?

More or less yes, it depends on what creates the negative cash flow. Generally speaking the long run relationship between rents and house prices can be expressed as follows;

$$R\_t = P\_t[(i\_t + τ p\_t )(1 − τ y\_t ) + δ\_t + λ\_t − E\_tG\_{t+1}], \tag{\*}$$

where $i\_t$ is the real interest rate, $τ p\_t$ is the property tax rate, $τ y\_t$ is the marginal
income tax rate, $δ\_t$ is the combined maintenance and depreciation rate, $λ\_t$ is the risk premium associated with housing, and $E\_tG\_{t+1}$ is expected capital gains ([Gallin 2004](https://www.federalreserve.gov/pubs/feds/2004/200450/200450pap.pdf)).

The cashflow that someone who owns and rents a house would get would be in essence;

$$R\_t - P\_t[(i\_t + τ p\_t )(1 − τ y\_t ) - m\_t] =CF(P)$$

where $m\_t$ is portion of $\delta$ spent on maintenance ($d\_t$ is portion that is depreciation). Next the we can rearrange \* and solve for capital gains to get;

$$-\frac{R\_t - P\_t[(i\_t + τ p\_t )(1 − τ y\_t ) - m\_t] }{P\_t} -d\_t - \lambda = E\_tG\_{t+1}, \tag{\*\*}$$

Or;

$$-\frac{CF(P\_t) }{P\_t} -d\_t - \lambda = E\_tG\_{t+1}$$

The equation above shows, that if the cashflow is higher then the expected capital gains from the houses are lower. However, there is a caveat. The cash flow depends negatively on $P$ but $P$ is both in numerator and denominator. Hence, if the negative cash flow is due to fall in rents, increase in interest rate, taxes or maintenance yes, if due to increase in the house price the effect depends on whether the change in numerator dominates the change in denominator.

> Can it be implied by the efficient market hypothesis (EMH) and the fact that these properties otherwise yield a relatively low ROI that this higher rate of appreciation will likely continue?

I do not see how that is implied by EMH. First, efficient market hypothesis is typically a hypothesis that is applied to stock markets. Theoretically you could apply it to other asset prices I suppose but to my best knowledge it is not applied to housing market. However, suppose we were to apply it housing market.

Efficient market hypothesis just says that asset prices are unpredictable because all avaiable information is already 'priced in' the price of asset. That is not the same as saying the price of asset does not depend on some fundamentals. It just means that all knowledge about the fundamentals is already reflected in the price so any price change is due to some new unexpected information. Inasmuch I can't see how this would violate EMH if applied to house prices. EMH doesn't claim there won't be trend in the aggregate prices. It just claims the individual prices will follow random walk around a trend given by fundamentals.

Also, your question makes it seems like Cambridge house prices always increase by 0.5% faster, but your own data show that is clearly not the case. Your own data you linked show that the prices in Cambridge sometimes increase faster sometimes slower than in rest of the England. In fact I am not even sure where yo got the 0.5% figure. The [site](https://www.ons.gov.uk/visualisations/housingpriceslocal/E07000008/) you used as a source does not mention that.

> He also states that he's almost 100% sure that the housing market would drop, which also seems to violate the EMH.

Again not sure how this would violate EMH. I am almost 100% sure stock market will be increasing on average over next 50 years. Neither Sal's or mine obesrvation violates EMH. EMH says the price of individual asset is unpredictable, it doesn't say you cannot predict long term trends on stock market etc. You just can't do better than market on average.

> **Comments:**
> **username_0**: The EMH implies than consistent alpha generation is impossible. There are indirect ways you could short the housing market if you knew it was going down to achieve alpha, no? Or without making a formal arbitrage argument: If there is not an appreciation premium, then these housing markets have negative alpha, so why would firms invest in them?  
> **username_1**: @username_0 yes because alpha is measure for active investments, not passive tracking of the market. EMH does not say it’s not possible to earn return by investing into stock market. It just says you cannot earn more than normal return.  

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