Key Concepts 🤔

‣

Yield Gap 📊

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Segmented Markets Theory for Bonds

Documents

L3 Reading - Cornerstone Cap-rates-and-RE-Cycles.pdf

L3 Reading - Cornerstone Cap-rates-and-RE-Cycles.pdf690.3KB

📊 Google Sheets for Calculations ← Link here 🧠

Acronyms 🤯

DCR → Debt Coverage Ratio

CPM → Capital Payment Method

CPM = FPM → Financing Payment Method

Old Exams

Exam-AI2153_2023-01-15_facit.pdf674.1KB

Exam-AI2153_2022-01-14_facit.pdf427.3KB

AI2153 20210115 tenta+svar betyg A.pdf380.2KB

AI2153 20210406 omtenta+betyg A.pdf331.4KB

Formulas ✖️➗

Cap Rate

\text{Cap rate} = \frac{\text{NOI}}{\text{(Price or Value)}} \\ \text{Cap rate} = r - g \\ \text{Cap rate}= \text{Real rate (riskfree)} + \text{inflation rate} + \text{risk premia} - (\text{real growth rate of NOI} + \text{inflation rate})

Yield Gap

\textup{Yield Gap = } (\textup{Cap rate} - k_{rf}) \\ k_{rf} = \textrm{ Yield on government bonds} \\ (\textup{Cap rate} - k_{rf}) \approx (RP - g) \\

Cap Rate Level Determinants

\textup{Cap rate} \approx (k_{rf} + RP) - g \\ k_{rf} = \textrm{ Yield on 10 year government bonds} \\ RP = \textrm{Real Estate Risk Premium} \\ g = \textrm{Property Income Growth Expectations}

Cap Rate Spread Determinants

(\textup{Cap rate} - k_{rf}) \approx (RP - g) \\ k_{rf} = \textrm{ Yield on government bonds} \\ RP = \textrm{Real Estate Risk Premium} \\ g = \textrm{Property Income Growth Expectations}

Federal Funds Rate formula - Taylor Rule

\text{Federal Funds Target Rate} = \text{Equilibrium Real Fed Funds Rate} + \text{Observed Inflation} + 0.5 \times (\text{Inflation Gap}) + 0.5 \times (\text{Output Gap}) \\ \text{where} \\ \text{Inflation Gap} = \text{Observed Inflation} - \text{Target Inflation} \\ \\ \text{Output Gap} = \frac{\text{Actual GDP} - \text{Potential GDP}}{\text{Potential GDP}}

Exam AI2153 - January 14, 2023

Q1 - Calculate Cap Rate with the level determinants

You analyze the evolution of cap rates (initial yields) in the real estate market by breaking down the cap rate into its core determinants (ignoring the depreciation effect). Suppose that the real risk-free on government bonds is 2.0%, the expected inflation rate is 2.5%, the risk premium is 3.5%, and the cap rate (initial yield) is 3.5%.

Then the real growth rate of property income (e.g. the net operating income) is closest to

A) 0.0%.

B) 7.5%.

C) 2.0%.

D) –2.0%.

E) None of the above (A, B, C, D) is close to be correct.

🧠

Cap Rate = (k + RP) - g k = 2% RP = 3,5% g = Initial Yield = 3,5% Cap Rate = (2 + 3,5) - 3,5 = 2% Krf=2% RP = 6% g = 1% cap Rate = (2%-6%)-1% = -5%

✅

Answer = 2% → C) 2.0%

Q2 - Find flaws in how they word formulas

In the Cornerstone report Lecture 3, Nov 9 -Cap-rates-and-RE-Cycles.pdf you can find some interesting formulas. One formula is the “cap rate spread” → (Cap Rate - k) ≈ (RP - g)

Which of following statements is not correct (i.e. is false)?

A) The left-hand side of the formula “cap rate spread” is the formula that is used to calculate the “yield gap” in the diagram.

C) The yield gap in the diagram is negative when the 10-year nominal government bond interest rate is higher than the Stockholm CBD prime office yield.

D) Both the yield gap and the cap rate spreads are positively related to the risk premium.

🧠

A) The left-hand side of the formula → (Cap Rate - k) is used to calculate yield gap → Yield gap refers to the difference between the yield (or return) on real estate investments and the yield on risk-free investments, such as government bonds. Answer is TRUE

✅

B) Although the Nordanö report writes that the yield gap is a measure of the risk premium for property, the Cornerstone report states that it is too simplistic to call the spread between cap rates and treasury yields a risk premium because the cap rate spread is equal to the risk premium plus the property income growth expectations. Formula - Cap Rate Spread: (cap Rate - k) = ( RP - g) What the underlined text states: (cap Rate - k) = ( RP + g) B) Is the false alternative

🧠

C) The yield gap in the diagram is negative when the 10-year nominal government bond interest rate is higher than the Stockholm CBD prime office yield. → if (k > cap rate) then the yield gap turns negative.

🧠

D) Both the yield gap and the cap rate spreads are positively related to the risk premium. Formula - Cap Rate Spread: (cap Rate - k) = ( RP - g) If RP increases, so should the cap rate spread - Therefore yield gap and cap rate spreads are positively related to risk premium

Q3 - Break Down words into a formula and

In the Nordanö report Lecture 3, Nov 9 - Nordanö - 2018-1_property-the-holy-grail-of-investments.pdf, you can find following diagram:

Which of following statements is not correct (i.e. is false)?

A) The real yield gap is equal to the nominal government bond interest rate + (expected) inflation rate minus the Stockholm CBD price office yield.

B) Nordanö argues that although Stockholm CBD office yields are record low (year 2018), investors still find office property investments attractive since the real yield gap has widened.

C) Inflation-linked bonds reflect the size of the real interest rate.

D) The real interest rate has fallen from about 4% in 1999 to below zero about 15 years later.

✅

A) The real yield gap is equal to the nominal government bond interest rate + (expected) inflation rate minus the Stockholm CBD price office yield. Nominal government bond interest rate = Bond that does not adjust interest payments based on inflation Expected Inflation = A guess on inflation, not the real inflation number CBD Price office Yield = Should be prime office yield for this one to make sense. “Real Yield Gap” = (Nominal Government bond + Expected inflation) - Yield This is not the formula, also the real yield gap cannot be derived from a formula that has an “expected” term in it. A is the false statement.

🧠

B) Nordanö argues that although Stockholm CBD office yields are record low (year 2018), investors still find office property investments attractive since the real yield gap has widened. → This is true, look at the graph

C) Inflation-linked bonds reflect the size of the real interest rate. → This statement true.

D) The real interest rate has fallen from about 4% in 1999 to below zero about 15 years later. → This is true, look at the graph

Q4 - Direct capitalization method of real estate valuation, with Cap Rate = 0

In the Cornerstone report Lecture 3, Nov 9 -Cap-rates-and-RE-Cycles.pdf you can find some interesting formulas. Suppose that the first year NOI for your private favorite property investment is USD 900 000. You compute the value of your property using the “direct capitalization” method of real estate valuation.

💼

Case 1: The real 5-year government bond interest rate is –0.5% (i.e. minus 0.5%). The (expected) inflation rate is 4.5%. The risk premium (RP) is 3.5%. Property income growth expectations (g) is 2.5%.

💼

Case 2: The real 5-year government bond interest rate is –1.5% (i.e. minus 1.5%). The (expected) inflation rate is 4.5%. The risk premium (RP) is 3.5%. Property income growth expectations (g) is 2.5%.

Which of following statements is correct (i.e. is true)?

A) The property value in case 1 is 20% higher than the property value in case 2.

B) The property value in case 1 is 25% higher than the property value in case 2.

C) The property value in case 2 is 20% higher than the property value in case 1.

D) The property value in case 2 is 25% higher than the property value in case 1.

E) None of the above (A, B, C, D) is close to be correct.

Solution Q4

Variables	Case 1	Case 2
Bond (rf)	-0.5%	-1.5%
Inflation	4.5%	4.5%
Risk Prem. (RP)	3.5%	3.5%
Growth (g)	2.5%	2.5%
NOI	900 000	900 000
Cap rate	0.5%	-0.5%
Property Value	180 mUSD	-180 mUSD

\textup{Cap rate} \approx (k_{rf} + RP) - g \\ k_{rf} = \textrm{ Yield on 10 year government bonds} \\ RP = \textrm{Real Estate Risk Premium} \\ g = \textrm{Property Income Growth Expectations}

\text{Value of Property} = \frac{\text{Net Operating Income (NOI)}}{\text{Capitalization Rate (Cap Rate)}}

✅

With a negative cap rate for case 2, we get a negative property value. Therefore Value of property on case (1) we get E) None of the above (A, B, C, D) is close to be correct.

Q5 - Calculate Expected IRR, Risk analysis, Variance, Standard Deviation

A property can be purchased for 15 000 000 today. A real estate analyst who likes risk analysis is analyzing the expected IRR and risk, measured as the standard deviation, of the real estate investment by projecting five different scenarios as follows:

Case	NOI	Selling Price (Y6)	Probability (P)
Severe recession	NOI will be 900 000 the first year, and then decrease 3.5 percent per year until year six.	10 000 000	5%
Moderate recession	NOI will be 900 000 the first year, and then decrease 1.5 percent per year until year six.	12 000 000	15%
Baseline forecast	NOI will be level 900 000 per year for the next six years.	16 000 000	35%
Moderate expansion	NOI will be 900 000 the first year, and then increase by 2.0 percent per year until year six.	18 000 000	30%
Strong boom expansion	NOI will be 900 000 the first year, and then increase 3.0 percent per year until year six.	20 000 000	15%

A) The expected IRR is 7.10 % and the standard deviation is 2.91 %.

B) The expected IRR is 7.10 % and the standard deviation is 0.084 %.

C) The expected IRR is 2.91 % and the standard deviation is 7.10 %.

D) The expected IRR is 0.084 % and the standard deviation is 7.10%.

E) None of the above (A, B, C, D) is close to be correct.

	Prob (P)	Growth YoY (g)	NOI Y0	NOI Y1	NOI Y2	NOI Y3	NOI Y4	NOI Y5	1️⃣ NOI Y6 (Sale + CF6)	2️⃣ IRR Scenarios	4️⃣ Scenario Variance
Severe recession	5%	-3.50%	-15000000	900000	868500	838103	808769	780462	10753146	-0.07%	0.03%
Moderate recession	15%	-1.50%	-15000000	900000	886500	873203	860104	847203	12834495	2.67%	0.03%
Baseline forecast	35%	0%	-15000000	900000	900000	900000	900000	900000	16900000	6.93%	0.00%
Moderate expansion	30%	2%	-15000000	900000	918000	936360	955087	974189	18993673	8.94%	0.01%
Strong boom expansion	15%	3%	-15000000	900000	927000	954810	983454	1012958	21043347	10.66%	0.02%
6️⃣ Standard Deviation										3️⃣ Mean IRR (Expected IRR)	5️⃣ Variance
2.91%										7.10%	0.08%

1️⃣ Future Value Cashflow

To calculate NOI for year 1→6

2️⃣ Calculate IRR for all scenarios📗

=IRR((NOI Year Zero:NOIY6))

Obs → NOI Year zero måste vara negativt för att IRR formeln ska funka i excel/sheets

3️⃣ Calculate Mean IRR (Expected IRR) 📗

The sum of all scenarios based on their probability (Scenario probability)*(Case IRR)

=SUMPRODUCT(Scenario Prob(1->5);IRR(1->5))

4️⃣ Calculate Variance for each Case📗

=Scenario Prob.*((IRR for case)-(expected IRR))^2

5️⃣ Calculate Variance of Scenarios 📗

=sum(all case Variances) --> Variance

6️⃣ Standard Deviation 📗

=SQRT(Variance)

5️⃣ Variance	0,08%
6️⃣ Standard Deviation	2,91% ✅

🧠

Standard Deviation = 2,506%, Expected IRR = 7,10%

✅

Answer: A) The expected IRR is 7.10 % and the standard deviation is 2.91 %.

Q6 - Standard Deviation of NPV

MCQ 5 continued. If the required rate of return (the discount rate) is 12 % for each of the five scenarios in MCQ 5, then the standard deviation of the NPV is what?
A) ‒1 545 432.
B) 12 %.
C) 2 985 884
D) 1 545 432 .
E) None of the above (A, B, C, D) is close to be correct.

Econ. Forecast	Prob (P)	Growth (g)	1️⃣ NOI Y1	1️⃣ NOI Y2	1️⃣ NOI Y3	1️⃣ NOI Y4	1️⃣ NOI Y5	1️⃣ NOI Y6	Selling Price (Y6)
Severe	5%	-3.50%	900000	868500	838103	808769	780462	753146	10000000
Moderate	15%	-1.50%	900000	886500	873203	860104	847203	834495	12000000
Baseline	35%	0%	900000	900000	900000	900000	900000	900000	16000000
Moderate	30%	2%	900000	918000	936360	955087	974189	993673	18000000
Strong boom	15%	3%	900000	927000	954810	983454	1012958	1043347	20000000

Probability (P)	Price of prop.	NOI Y1 2️⃣	NOI Y2 2️⃣	NOI Y3 2️⃣	NOI Y4 2️⃣	NOI Y5 2️⃣	NOI Y6 2️⃣	SALE PRICE	PV SALE 3️⃣	PV Cashflow	PV SALE + CF 4️⃣	NPV 5️⃣	Variance 7️⃣
5%	-15000000	803571	692363	596545	513987	442855	381567	10,000,000	5,066,311.21	3,430,888.60	8,497,199.81	-6,502,800.19	618435128712
15%	-15000000	803571	706712	621528	546612	480726	422781	12,000,000	6,079,573.45	3,581,930.77	9,661,504.22	-5,338,495.78	830217637027
35%	-15000000	803571	717474	640602	571966	510684	455968	16,000,000	8,106,097.94	3,700,266.59	11,806,364.53	-3,193,635.47	15106299296
30%	-15000000	803571	731824	666483	606975	552781	503426	18,000,000	9,119,360.18	3,865,059.64	12,984,419.82	-2,015,580.18	282446595727
15%	-15000000	803571	738999	679615	625003	574780	528592	20,000,000	10,132,622.42	3,950,559.46	14,083,181.89	-916,818.11	642154774553
												Expected NPV 6️⃣	Variance 8️⃣
												-$2,985,883.56	2388360435315
													Standard dev. 8️⃣
													1,545,432.12

1️⃣ Calculate Future Value Cashflow for all scenarios📗

Calculate NOI for year 1→6

Future Value of Cashflows

See Table with Yellow Header

2️⃣ Discount future cashflow for all scenarios to PV 📗

Future Value Cashflows from first table are discounted to present value.
Given Discount Rate = 12%

See table with blue header

\text{DCF} = \sum_{t=1}^{n} \frac{\text{CF}_t}{(1 + r)^t}

‣

Explain formula pls

3️⃣ Calculate Present Value of property Sale and 📗

→ Given Discount Rate = 12%

\text{PV} = \frac{\text{FV}}{(1 + r)^n}

‣

Explain formula pls

4️⃣ Sum of Discounted Cashflows + Sale of property 📗

PV cashflow = Sum( NOI Y1 → NOI Y6)

PV (SALE & CF) = PV Cashflow + PV Sale

5️⃣ Calculate NPV for Each Scenario 📗

🧠 We bought the property for 15 000 000 USD.

NPV = (PV SALE + CF 4️⃣ )-15 000 000

Do this for scenario 1-5.

6️⃣ Calculate Mean NPV (Expected NPV) 📗

=SUMPRODUCT(Scenario Prob(1->5);NPV(1->5))

✅ Expected NPV = -$2,985,883.56

7️⃣ Calculate Variance for each Scenario

=Scenario Prob.*(((NPV for case)-(expected NPV))^2)

Here we get very large numbers

8️⃣ Sum Variances and Calculate Standard Deviation 📗

=sum(all case Variances) --> Variance

Standard Deviation

=SQRT(Variance) Voila! 👇

Expected NPV 6️⃣	Variance 8️⃣
-$2,985,883.56	2388360435315
	Standard dev. 8️⃣
	1,545,432.12

Q7 - Compute Arithmetic Mean of inflation in the US over 6 years.

Below is a list of annual US CPI values for urban consumers for the years 2015 – 2021.

Year	CPI All urban consumers
2015	237
2016	240
2017	245
2018	251
2019	256
2020	259
2021	271

Using these values, the average (arithmetic mean) annual rate of inflation over this period is:

A) 14.35%.

B) 2.27%.

C) 4.63%.

D) 2.05%.

E) None of the above (A, B, C, D) is close to be correct.

Year	CPI All urban consumers	1️⃣ Inflation YoY	🧮 In Excell
2015	237
2016	240	1.27%	=(240-237)/237
2017	245	2.08%	=(245-240)/240
2018	251	2.45%	etc…
2019	256	1.99%
2020	259	1.17%
2021	271	4.63%

	2️⃣ Mean	2.27%

1️⃣ Calculate Inflation YoY (Simple)📗

Inflation YoY = (CPI Y1 - CPI Y0) / (CPI Y0)

=(data Q(n+1)-data Q(n))/data Q(n)

2️⃣ Compute Arithmetic Mean📗

Arithmetic Mean = Average = Medelvärde

=average(Select Inflation start: Last inflation number)

✅

B) 2.27% is the correct answer

Q8 - Calculate the Five-Year Bond based on the the expected return on the One-Year Bond

If 1-year interest rates (proxy for short-term interest rates) for the next five years are expected to be 0.2, 0.5, 0.8, 1, and 1.5 percent, and the 5-year term premium is 0.5 percent, then the 5-year bond rate will be what?

Then the 5-year bond rate will be what?

A) 1.3%.

B) 0.8%.

C) 1.5%.

D) 2.1%.

E) None of the above (A, B, C, D) is close to be correct.

1️⃣ Calculate Mean 1Y-Bond

Calculate the mean of the bond

Mean = Average(Y1:Y5)

	One Year Bond
Y1	0,2%
Y2	0,5%
Y3	0,8%
Y4	1%
Y5	1.5%
Mean	0.8%

2️⃣ Calculate Five Year Bond

Five Year Bond = Mean + Premium

Five Year Bond: 0.8% + 0.5% = 1,3%

✅

A) 1,3%

Q9 - Present Value of equity for a property that was bought with Debt - (Solution in google Sheet)

⚠️

The sheet is named “Q9 Value of equity interest” - Link here!

The NOI for your income property is expected to be $900 000 for the first year. Debt financing will be based on a 1.2 DCR applied to the first year NOI, will have a 4.5 percent interest rate, and will be amortized over 30 years with monthly payments. This is a CPM (FPM), constant or fixed payment mortgage. The NOI will increase 2.5 percent per year after the first year. You expect to hold the property for five years. The resale price is estimated by applying a 4 percent terminal capitalization rate to the sixth-year NOI. You require a 12 percent rate of return on equity (equity yield rate) for your property. What is the present value of the equity interest in the property?

Note! If you choose MCQ alternative E, then you need to write the correct present value to get 1 point.

A) 10 964 278

B) 7 783 371

C) Minus 560 059

D) 11 152 667

E) None of the above (A, B, C, D) is close to be correct. Instead it should be: 8 752 513

	Values to plug into Google Sheets
NOI	900000
DCR	1.2
Interest Rate (i)	4.5%
Terminal Cap Rate	4%
Amortization 30 Years (n)	30
Hold time (q)	5 Years
Growth NOI (g)	2.5%
Equity Rate of return (R)	12%

Q10 - Example Essay Question

As you know, there exist many property sectors (with subsectors), see for instance REIT Sectors | Nareit (https://www.reit.com/what-reit/reit-sectors). Suppose you must choose only one sector to invest in (for some years). Which sector would you choose and why?

⚠️

I haven’t answered this question myself, but it’s included for your convenience

Exam Jan 15 2023

Q1 - Real growth on property Income given riskfree rate, cap rate and risk premium

You analyze the evolution of cap rates (initial yields) in the real estate market by breaking down the cap rate into its core determinants (ignoring the depreciation effect). Suppose that the real risk-free on government bonds is 2.0%, the expected inflation rate is 2.5%, the risk premium is 3.5%, and the cap rate (initial yield) is 3.5%.

Then the real growth rate of property income (e.g. the net operating income) is closest to

A) 0.0%.

B) 7.5%.

C) 2.0%.

D) –2.0%.

E) None of the above (A, B, C, D) is close to be correct.

✅

See formula to the right —> —> —> Cap Rate - Krf = RP - G Krf = 2% RP = 3,5% Cap rate = 3,5% → 3,5 - 2 = 3,5 - g → g = 3,5 - 3,5 + 2 → g = 2% Answer: g = 2% C) 2.0%

(\textup{Cap rate} - k_{rf}) \approx (RP - g) \\ k_{rf} = \textrm{ Yield on government bonds} \\ RP = \textrm{Real Estate Risk Premium} \\ g = \textrm{Property Income Growth Expectations}

Q2 & Q3 -

Corporate bonds and interest rates are highly important for real estate companies. Suppose that you invest in corporate bonds issued by a real estate company today with 10 years to maturity. The coupon rate is 5% and coupons are paid annually. The face value is $1,000 (One thousand). The yield to maturity (YTM) is currently 5%. Corporate bonds and interest rates are highly important for real estate companies. Suppose that you invest in corporate bonds issued by a real estate company today with 10 years to maturity. The coupon rate is 5% and coupons are paid annually. The face value is $1,000 (One thousand). The yield to maturity (YTM) is currently 5%.

2) When you buy the bond today, its price is

A) equal to the face value.

B) lower than the face value.

C) higher than the face value.

D) Since the YTM is equal to the coupon rate, it is not possible to compute the price of the bond.

E) None of the above (A, B, C, D) is close to be correct.

✅

When buying a bond, the value of the bond is equal to face value. Eg. It is marked to market.

3) One year later, the yield to maturity on your bond investment has declined to 4%. After one year, the total rate of return of your bond investment is closest to?

A) 0.0%.

B) 4.3%.

C) –9.3%.

D) 9.3%.

E) None of the above (A, B, C, D) is close to be correct.

✅

Ask ChatGPT to solve this in python and you can conclude that E) None of the above (A, B, C, D) is close to be correct.

‣

Solution by ChatGPT in python

Q4 -

The following diagram from FRED shows the spread between US 10-Year Treasury Constant Maturity and the US 3-Month Treasury Constant Maturity. The following diagram from FRED shows the spread between US 10-Year Treasury Constant Maturity and the US 3-Month Treasury Constant Maturity. What can you tell about the current shape of the US treasury yield curve?

What can you tell about the current shape of the US treasury yield curve?

A) flat.

B) upward sloping.

C) downward sloping.

D) not inverted

E) None of the above (A, B, C, D) is close to be correct.

Q5

If 1-year interest rates (proxy for short-term interest rates) for the next five years are expected to be 5.5, 5.0, 4.5, 4.0, and 4.0 percent, and the 5-year term premium (aka the liquidity premium) is 1 percent, then the 5-year bond rate will be closest to

A) 4.6 percent.

B) 3.6 percent.

C) 5.6 percent.

D) 4 percent.

E) None of the above (A, B, C, D) is close to be correct.

Q6

A property is expected to have NOI of $500,000 the first year. The NOI is expected to increase by 2 percent per year thereafter. The appraised value of the property is currently $8 million, and the lender is willing to make a $5,600,000 participation loan with a contract interest rate of 7 percent. The loan, a constant (or fixed) payment mortgage) will be amortized with monthly payments over a 25-year term. In addition to the regular mortgage payments, the lender will receive 40 percent of the NOI in excess of $500,000 each year until the loan is repaid. The lender also will receive 60 percent of any increase in the value of the property. The loan includes a substantial prepayment penalty for repayment before year 5, and the balance of the loan is due in year 10. (If the property has not been sold, the participation will be based on the appraised value of the property.) Assume that the appraiser would estimate the value in year 10 by dividing the NOI for year 11 by a 5 percent capitalization rate.

The effective cost (to the borrower) of the participation loan assuming the loan is held for 10 years will be closest to

A) 10.22 percent.

B) 3.6 percent.

C) 7.56 percent.

D) 7.48 percent.

E) None of the above (A, B, C, D) is close to be correct. Instead it should be___________

Q7 - ESSAY Question (with Answer)

Following diagram from FRED (see next page please) is very famous among professionals, practitioners and academicians interested in how monetary policy affects the global economy including the pricing and valuation of financial and real assets:

Based on your great knowledge, discuss and explain how the evolution of commercial real estate cap rates, prices and valuations of commercial real estate, and prices and valuation of financial securities such as corporate bonds and listed real estate (e.g. REITs and publicly traded real estate companies) might be related to the above diagram.

✅

This diagram shows the total assets of the Federal Reserve, where securities held outright by the Federal Reserve make out the largest part. The Fed controls their own balance sheet and adjusts it to steer interest rates, meet their inflation target, and stable the currency of the United States (USD). They can either buy or sell assets as measures to control their balance sheet. The largest assets held by the FED are Treasury notes and bonds, and mortgage-backed securities, which are debt instruments used to raise capital. When the FED buys large amounts of these assets (Quantitative Easing) the prices of these assets go up, and long-term interest rates fall (yields on government bonds decrease), as a result, loaning and investing are incentivized. This is done to support a weak economical situation, such as the financial crisis of 2008 or during the pandemic starting in 2020, which can be seen in the diagram above.

Since the availability of money increases due to Quantitative Easing (QE), the demand to invest in assets such as real estate and bonds, publicly traded real estate companies, and REITs increases for investors.

Historically, this has led to higher valuations for real estate, stocks, corporate bonds, and REITs. The reason for higher valuations is that yields (cap rates for real estate) shrink as a result of lower financing costs, meaning that the investors’ cashflow models can “accept” lower yields (higher purchasing prices) as the costs of financing decreases. Also, cap rate could be calculated with the yield spread formula (cap rate = yield on government bonds + risk premium – nominal growth rate), earlier I said that QE leads to lower yields for government bonds, this would imply that cap rates for real estate also decline. In a booming market (as a result of QE), this can then lead to investors racing towards a smaller and smaller spread between individual interest rates and yields, by purchasing the assets at a higher and higher valuation, as they want to acquire as much as possible to maximize their cash return.

As publicly traded real estate companies and REITs’ valuations could be assessed based on their real estate portfolio (using for example the NAV discount/premium method), it is logical that the prices and valuations on them also increase as the cap rate of their portfolio declines.

To conclude, historical periods of sharp increases in the FED-held assets (financial crisis of 2008 or during the pandemic starting in 2020) have led to subsequent periods of declining yields and increasing valua valuations of assets in general, which in short could be explained by for example increased demand to invest.

AI2153 - Financial Economics with Real Estate Applications

Documents

📊 Google Sheets for Calculations ← Link here 🧠

Formulas ✖️➗

Exam AI2153 - January 14, 2023

Q1 - Calculate Cap Rate with the level determinants

Q2 - Find flaws in how they word formulas

Q3 - Break Down words into a formula and

Q4 - Direct capitalization method of real estate valuation, with Cap Rate = 0

Q5 - Calculate Expected IRR, Risk analysis, Variance, Standard Deviation

Q6 - Standard Deviation of NPV

Q7 - Compute Arithmetic Mean of inflation in the US over 6 years.

Q8 - Calculate the Five-Year Bond based on the the expected return on the One-Year Bond

Q9 - Present Value of equity for a property that was bought with Debt - (Solution in google Sheet)

Q10 - Example Essay Question

Exam Jan 15 2023

Q1 - Real growth on property Income given riskfree rate, cap rate and risk premium

Q2 & Q3 -

Q4 -

Q5

Q6

Q7 - ESSAY Question (with Answer)