Alex: Hi, Brian. I would like to ask you about leverage. The Professor was talki

Question

Alex: Hi, Brian. I would like to ask you about leverage. The Professor was talking about the advantages and disadvantage of banks using leverage. From what I understand, high bank leverage was one of the key ingredients in the housing bubble and the financial crisis that followed. What I do not understand is that, if leverage is so risky, why wouldn't the government just forbid banks from using leverage at all and thus eliminate the possibility of such a crisis in the future? BRIAN: Alex, this is not an easy question. Regulators and bankers are still searching for strategies that would benefit both investors and bank customers. I'll try to help you understand the trade-off of using leverage versus abandoning it completely. But first, let's make sure you understand what leverage is. ALEX: In banking, leverage means that banks can use reserves to purchase assets that offer higher returns and thus increase the potential return on. BRIAN: Consider a bank that has $6,000,000 in deposits and $2,000,000 in reserves. Suppose it lends out $5, 400,000. What are the bank's total assets and stockholders' equity? ALEX: This bank has $ in assets, and stockholders' equity is $ BRIAN: Now, suppose the bank's deposits carry an average annual interest rate of 2%, whereas its loans yield 4%. This means that the bank earns $5, 400,000 times 0.04 = $216,000 on loans and must pay only $6,000,000 times 0.02= $120,000 in interest on deposits. To sum up, the bank "borrowed" dollar deposits from its customers to return $216,000 -$120,000 = $96,000 per year in profit for its stockholders. ALEX: I see. This implies that the bank offers a return of % on its equity of $1, 400,000. Quite impressive! BRIAN: Yes, the investors should be excited to get such a return! However, what if there is a spate of defaults, so that the bank's assets (loans) fall in value by, say, 10%, or $5, 400,000 times 0.1 = $540,000? The value of loans outstanding would decline to $5, 400,000 - $540,000 = $4, 860,000, and total assets would be $2,000,000+ $4, 860,000 = $6, 860,000. Consequently, the stockholders' equity will decline to $6, 860,000 -$6,000,000= $860,000. ALEX: But this means that the bank's shareholders lost % of the original equity of $1, 400,000! BRIAN: Now, let's see whether it would really help if the bank used no leverage, that is, if it operated without borrowing from customer deposits. All it would be able to loan out is its equity of $1, 400,000, which would earn just $1, 400,000 times 0.04 = $56,000. Given a 2% interest rate on deposits, the bank's profit would be $56,000 - $120,000= -$64,000. With such low expected returns, the bank would not exist in the first place, as investors would undoubtedly go somewhere else. Thus leverage is essential to a bank's profitability, but it also carries significant risk.

Explanation / Answer

In banking, leverage means that bank can use reserves to purchase assets and thus increase the potential return on investment.

Consider a bank that has $6000000 in deposits and $2000,000 in reserves. Suppose it lends out $5400000, the bank’s total assets = $5,400,000 and shareholder equity $1,400,000

=(96000/1400000) *100 = 6.85%

=(860000/1400000) *100 = 61.42%

100 – 61.42 = 38.58%

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